,,the ,,problems ,,of ,,philosophy ,by ,bertrand ,russell ,,preface ,in the following pages ,i have confined myself in the main to those problems of philosophy in regard to which ,i thought it possible to say something positive and constructive1 since merely negative criticism seemed out of place4 ,for this reason1 theory of knowledge occupies a larger space than metaphysics in the present volume1 and some topics much discussed by philosophers are treated very briefly1 if at all4 ,i have derived valuable assistance from unpublished writings of ,g4 ,e4 ,moore and ,j4 ,m4 ,keynes3 from the former1 as regards the relations of sense-data to physical objects1 and from the latter as regards probability and induction4 ,i have also profited greatly by the criticisms and suggestions of ,professor ,gilbert ,murray4 #aiab ,,chapter ,i4 ,,appearance ,,and ,,reality ,is there any knowledge in the world which is so certain that no reasonable man could doubt it8 ,this question1 which at first sight might not seem difficult1 is really one of the most difficult that can be asked4 ,when we have realized the obstacles in the way of a straightforward and confident answer1 we shall be well launched on the study of philosophy--for philosophy is merely the attempt to answer such ultimate questions1 not carelessly and dogmatically1 as we do in ordinary life and even in the sciences1 but critically1 after exploring all that makes such questions puzzling1 and after realizing all the vagueness and confusion that underlie our ordinary ideas4 ,in daily life1 we assume as certain many things which1 on a closer scrutiny1 are found to be so full of apparent contradictions that only a great amount of thought enables us to know what it is that we really may believe4 ,in the search for certainty1 it is natural to begin with our present experiences1 and in some sense1 no doubt1 knowledge is to be derived from them4 ,but any statement as to what it is that our immediate experiences make us know is very likely to be wrong4 ,it seems to me that ,i am now sitting in a chair1 at a table of a certain shape1 on which ,i see sheets of paper with writing or print4 ,by turning my head ,i see out of the window buildings and clouds and the sun4 ,i believe that the sun is about ninety-three million miles from the earth2 that it is a hot globe many times bigger than the earth2 that1 owing to the earth's rotation1 it rises every morning1 and will continue to do so for an indefinite time in the future4 ,i believe that1 if any other normal person comes into my room1 he will see the same chairs and tables and books and papers as ,i see1 and that the table which ,i see is the same as the table which ,i feel pressing against my arm4 ,all this seems to be so evident as to be hardly worth stating1 except in answer to a man who doubts whether ,i know anything4 ,yet all this may be reasonably doubted1 and all of it requires much careful discussion before we can be sure that we have stated it in a form that is wholly true4 ,to make our difficulties plain1 let us concentrate attention on the table4 ,to the eye it is oblong1 brown and shiny1 to the touch it is smooth and cool and hard2 when ,i tap it1 it gives out a wooden sound4 ,any one else who sees and feels and hears the table will agree with this description1 so that it might seem as if no difficulty would arise2 but as soon as we try to be more precise our troubles begin4 ,although ,i believe that the table is 'really' of the same colour all over1 the parts that reflect the light look much brighter than the other parts1 and some parts look white because of reflected light4 ,i know that1 if ,i move1 the parts that reflect the light will be different1 so that the apparent distribution of colours on the table will change4 ,it follows that if several people are looking at the table at the same moment1 no two of them will see exactly the same distribution of colours1 because no two can see it from exactly the same point of view1 and any change in the point of view makes some change in the way the light is reflected4 ,for most practical purposes these differences are unimportant1 but to the painter they are all-important3 the painter has to unlearn the habit of thinking that things seem to have the colour which common sense says they 'really' have1 and to learn the habit of seeing things as they appear4 ,here we have already the beginning of one of the distinctions that cause most trouble in philosophy--the distinction between 'appearance' and 'reality'1 between what things seem to be and what they are4 ,the painter wants to know what things seem to be1 the practical man and the philosopher want to know what they are2 but the philosopher's wish to know this is stronger than the practical man's1 and is more troubled by knowledge as to the difficulties of answering the question4 ,to return to the table4 ,it is evident from what we have found1 that there is no colour which pre-eminently appears to be the colour of the table1 or even of any one particular part of the table--it appears to be of different colours from different points of view1 and there is no reason for regarding some of these as more really its colour than others4 ,and we know that even from a given point of view the colour will seem different by artificial light1 or to a colour-blind man1 or to a man wearing blue spectacles1 while in the dark there will be no colour at all1 though to touch and hearing the table will be unchanged4 ,this colour is not something which is inherent in the table1 but something depending upon the table and the spectator and the way the light falls on the table4 ,when1 in ordinary life1 we speak of the colour of the table1 we only mean the sort of colour which it will seem to have to a normal spectator from an ordinary point of view under usual conditions of light4 ,but the other colours which appear under other conditions have just as good a right to be considered real2 and therefore1 to avoid favouritism1 we are compelled to deny that1 in itself1 the table has any one particular colour4 ,the same thing applies to the texture4 ,with the naked eye one can see the grain1 but otherwise the table looks smooth and even4 ,if we looked at it through a microscope1 we should see roughnesses and hills and valleys1 and all sorts of differences that are imperceptible to the naked eye4 ,which of these is the 'real' table8 ,we are naturally tempted to say that what we see through the microscope is more real1 but that in turn would be changed by a still more powerful microscope4 ,if1 then1 we cannot trust what we see with the naked eye1 why should we trust what we see through a microscope8 ,thus1 again1 the confidence in our senses with which we began deserts us4 ,the shape of the table is no better4 ,we are all in the habit of judging as to the 'real' shapes of things1 and we do this so unreflectingly that we come to think we actually see the real shapes4 ,but1 in fact1 as we all have to learn if we try to draw1 a given thing looks different in shape from every different point of view4 ,if our table is 'really' rectangular1 it will look1 from almost all points of view1 as if it had two acute angles and two obtuse angles4 ,if opposite sides are parallel1 they will look as if they converged to a point away from the spectator2 if they are of equal length1 they will look as if the nearer side were longer4 ,all these things are not commonly noticed in looking at a table1 because experience has taught us to construct the 'real' shape from the apparent shape1 and the 'real' shape is what interests us as practical men4 ,but the 'real' shape is not what we see2 it is something inferred from what we see4 ,and what we see is constantly changing in shape as we move about the room2 so that here again the senses seem not to give us the truth about the table itself1 but only about the appearance of the table4 ,similar difficulties arise when we consider the sense of touch4 ,it is true that the table always gives us a sensation of hardness1 and we feel that it resists pressure4 ,but the sensation we obtain depends upon how hard we press the table and also upon what part of the body we press with2 thus the various sensations due to various pressures or various parts of the body cannot be supposed to reveal directly any definite property of the table1 but at most to be signs of some property which perhaps causes all the sensations1 but is not actually apparent in any of them4 ,and the same applies still more obviously to the sounds which can be elicited by rapping the table4 ,thus it becomes evident that the real table1 if there is one1 is not the same as what we immediately experience by sight or touch or hearing4 ,the real table1 if there is one1 is not immediately known to us at all1 but must be an inference from what is immediately known4 ,hence1 two very difficult questions at once arise2 namely1 7#a7 ,is there a real table at all8 7#b7 ,if so1 what sort of object can it be8 ,it will help us in considering these questions to have a few simple terms of which the meaning is definite and clear4 ,let us give the name of 'sense-data' to the things that are immediately known in sensation3 such things as colours1 sounds1 smells1 hardnesses1 roughnesses1 and so on4 ,we shall give the name 'sensation' to the experience of being immediately aware of these things4 ,thus1 whenever we see a colour1 we have a sensation of the colour1 but the colour itself is a sense-datum1 not a sensation4 ,the colour is that of which we are immediately aware1 and the awareness itself is the sensation4 ,it is plain that if we are to know anything about the table1 it must be by means of the sense-data--brown colour1 oblong shape1 smoothness1 etc4--which we associate with the table2 but1 for the reasons which have been given1 we cannot say that the table is the sense-data1 or even that the sense-data are directly properties of the table4 ,thus a problem arises as to the relation of the sense-data to the real table1 supposing there is such a thing4 ,the real table1 if it exists1 we will call a 'physical object'4 ,thus we have to consider the relation of sense-data to physical objects4 ,the collection of all physical objects is called 'matter'4 ,thus our two questions may be re-stated as follows3 7#a7 ,is there any such thing as matter8 7#b7 ,if so1 what is its nature8 ,the philosopher who first brought prominently forward the reasons for regarding the immediate objects of our senses as not existing independently of us was ,bishop ,berkeley 7#afhe-agec74 ,his ,three ,dialogues between ,hylas and ,philonous1 in ,opposition to ,sceptics and ,atheists1 undertake to prove that there is no such thing as matter at all1 and that the world consists of nothing but minds and their ideas4 ,hylas has hitherto believed in matter1 but he is no match for ,philonous1 who mercilessly drives him into contradictions and paradoxes1 and makes his own denial of matter seem1 in the end1 as if it were almost common sense4 ,the arguments employed are of very different value3 some are important and sound1 others are confused or quibbling4 ,but ,berkeley retains the merit of having shown that the existence of matter is capable of being denied without absurdity1 and that if there are any things that exist independently of us they cannot be the immediate objects of our sensations4 ,there are two different questions involved when we ask whether matter exists1 and it is important to keep them clear4 ,we commonly mean by 'matter' something which is opposed to 'mind'1 something which we think of as occupying space and as radically incapable of any sort of thought or consciousness4 ,it is chiefly in this sense that ,berkeley denies matter2 that is to say1 he does not deny that the sense-data which we commonly take as signs of the existence of the table are really signs of the existence of something independent of us1 but he does deny that this something is non-mental1 that it is neither mind nor ideas entertained by some mind4 ,he admits that there must be something which continues to exist when we go out of the room or shut our eyes1 and that what we call seeing the table does really give us reason for believing in something which persists even when we are not seeing it4 ,but he thinks that this something cannot be radically different in nature from what we see1 and cannot be independent of seeing altogether1 though it must be independent of our seeing4 ,he is thus led to regard the 'real' table as an idea in the mind of ,god4 ,such an idea has the required permanence and independence of ourselves1 without being--as matter would otherwise be--something quite unknowable1 in the sense that we can only infer it1 and can never be directly and immediately aware of it4 ,other philosophers since ,berkeley have also held that1 although the table does not depend for its existence upon being seen by me1 it does depend upon being seen 7or otherwise apprehended in sensation7 by some mind--not necessarily the mind of ,god1 but more often the whole collective mind of the universe4 ,this they hold1 as ,berkeley does1 chiefly because they think there can be nothing real--or at any rate nothing known to be real except minds and their thoughts and feelings4 ,we might state the argument by which they support their view in some such way as this3 ',whatever can be thought of is an idea in the mind of the person thinking of it2 therefore nothing can be thought of except ideas in minds2 therefore anything else is inconceivable1 and what is inconceivable cannot exist4' ,such an argument1 in my opinion1 is fallacious2 and of course those who advance it do not put it so shortly or so crudely4 ,but whether valid or not1 the argument has been very widely advanced in one form or another2 and very many philosophers1 perhaps a majority1 have held that there is nothing real except minds and their ideas4 ,such philosophers are called 'idealists'4 ,when they come to explaining matter1 they either say1 like ,berkeley1 that matter is really nothing but a collection of ideas1 or they say1 like ,leibniz 7#afdf-agaf71 that what appears as matter is really a collection of more or less rudimentary minds4 ,but these philosophers1 though they deny matter as opposed to mind1 nevertheless1 in another sense1 admit matter4 ,it will be remembered that we asked two questions2 namely1 7#a7 ,is there a real table at all8 7#b7 ,if so1 what sort of object can it be8 ,now both ,berkeley and ,leibniz admit that there is a real table1 but ,berkeley says it is certain ideas in the mind of ,god1 and ,leibniz says it is a colony of souls4 ,thus both of them answer our first question in the affirmative1 and only diverge from the views of ordinary mortals in their answer to our second question4 ,in fact1 almost all philosophers seem to be agreed that there is a real table3 they almost all agree that1 however much our sense-data--colour1 shape1 smoothness1 etc4--may depend upon us1 yet their occurrence is a sign of something existing independently of us1 something differing1 perhaps1 completely from our sense-data1 and yet to be regarded as causing those sense-data whenever we are in a suitable relation to the real table4 ,now obviously this point in which the philosophers are agreed--the view that there is a real table1 whatever its nature may be--is vitally important1 and it will be worth while to consider what reasons there are for accepting this view before we go on to the further question as to the nature of the real table4 ,our next chapter1 therefore1 will be concerned with the reasons for supposing that there is a real table at all4 ,before we go farther it will be well to consider for a moment what it is that we have discovered so far4 ,it has appeared that1 if we take any common object of the sort that is supposed to be known by the senses1 what the senses immediately tell us is not the truth about the object as it is apart from us1 but only the truth about certain sense-data which1 so far as we can see1 depend upon the relations between us and the object4 ,thus what we directly see and feel is merely 'appearance'1 which we believe to be a sign of some 'reality' behind4 ,but if the reality is not what appears1 have we any means of knowing whether there is any reality at all8 ,and if so1 have we any means of finding out what it is like8 ,such questions are bewildering1 and it is difficult to know that even the strangest hypotheses may not be true4 ,thus our familiar table1 which has roused but the slightest thoughts in us hitherto1 has become a problem full of surprising possibilities4 ,the one thing we know about it is that it is not what it seems4 ,beyond this modest result1 so far1 we have the most complete liberty of conjecture4 ,leibniz tells us it is a community of souls3 ,berkeley tells us it is an idea in the mind of ,god2 sober science1 scarcely less wonderful1 tells us it is a vast collection of electric charges in violent motion4 ,among these surprising possibilities1 doubt suggests that perhaps there is no table at all4 ,philosophy1 if it cannot answer so many questions as we could wish1 has at least the power of asking questions which increase the interest of the world1 and show the strangeness and wonder lying just below the surface even in the commonest things of daily life4 ,,chapter ,,ii4 ,,the ,,existence ,,of ,,matter ,in this chapter we have to ask ourselves whether1 in any sense at all1 there is such a thing as matter4 ,is there a table which has a certain intrinsic nature1 and continues to exist when ,i am not looking1 or is the table merely a product of my imagination1 a dream-table in a very prolonged dream8 ,this question is of the greatest importance4 ,for if we cannot be sure of the independent existence of objects1 we cannot be sure of the independent existence of other people's bodies1 and therefore still less of other people's minds1 since we have no grounds for believing in their minds except such as are derived from observing their bodies4 ,thus if we cannot be sure of the independent existence of objects1 we shall be left alone in a desert--it may be that the whole outer world is nothing but a dream1 and that we alone exist4 ,this is an uncomfortable possibility2 but although it cannot be strictly proved to be false1 there is not the slightest reason to suppose that it is true4 ,in this chapter we have to see why this is the case4 ,before we embark upon doubtful matters1 let us try to find some more or less fixed point from which to start4 ,although we are doubting the physical existence of the table1 we are not doubting the existence of the sense-data which made us think there was a table2 we are not doubting that1 while we look1 a certain colour and shape appear to us1 and while we press1 a certain sensation of hardness is experienced by us4 ,all this1 which is psychological1 we are not calling in question4 ,in fact1 whatever else may be doubtful1 some at least of our immediate experiences seem absolutely certain4 ,descartes 7#aeif-afej71 the founder of modern philosophy1 invented a method which may still be used with profit--the method of systematic doubt4 ,he determined that he would believe nothing which he did not see quite clearly and distinctly to be true4 ,whatever he could bring himself to doubt1 he would doubt1 until he saw reason for not doubting it4 ,by applying this method he gradually became convinced that the only existence of which he could be quite certain was his own4 ,he imagined a deceitful demon1 who presented unreal things to his senses in a perpetual phantasmagoria2 it might be very improbable that such a demon existed1 but still it was possible1 and therefore doubt concerning things perceived by the senses was possible4 ,but doubt concerning his own existence was not possible1 for if he did not exist1 no demon could deceive him4 ,if he doubted1 he must exist2 if he had any experiences whatever1 he must exist4 ,thus his own existence was an absolute certainty to him4 ',i think1 therefore ,i am1' he said 7,cogito1 ergo sum72 and on the basis of this certainty he set to work to build up again the world of knowledge which his doubt had laid in ruins4 ,by inventing the method of doubt1 and by showing that subjective things are the most certain1 ,descartes performed a great service to philosophy1 and one which makes him still useful to all students of the subject4 ,but some care is needed in using ,descartes' argument4 ',i think1 therefore ,i am' says rather more than is strictly certain4 ,it might seem as though we were quite sure of being the same person to-day as we were yesterday1 and this is no doubt true in some sense4 ,but the real ,self is as hard to arrive at as the real table1 and does not seem to have that absolute1 convincing certainty that belongs to particular experiences4 ,when ,i look at my table and see a certain brown colour1 what is quite certain at once is not ',i am seeing a brown colour'1 but rather1 'a brown colour is being seen'4 ,this of course involves something 7or somebody7 which 7or who7 sees the brown colour2 but it does not of itself involve that more or less permanent person whom we call ',i'4 ,so far as immediate certainty goes1 it might be that the something which sees the brown colour is quite momentary1 and not the same as the something which has some different experience the next moment4 ,thus it is our particular thoughts and feelings that have primitive certainty4 ,and this applies to dreams and hallucinations as well as to normal perceptions3 when we dream or see a ghost1 we certainly do have the sensations we think we have1 but for various reasons it is held that no physical object corresponds to these sensations4 ,thus the certainty of our knowledge of our own experiences does not have to be limited in any way to allow for exceptional cases4 ,here1 therefore1 we have1 for what it is worth1 a solid basis from which to begin our pursuit of knowledge4 ,the problem we have to consider is this3 ,granted that we are certain of our own sense-data1 have we any reason for regarding them as signs of the existence of something else1 which we can call the physical object8 ,when we have enumerated all the sense-data which we should naturally regard as connected with the table1 have we said all there is to say about the table1 or is there still something else--something not a sense-datum1 something which persists when we go out of the room8 ,common sense unhesitatingly answers that there is4 ,what can be bought and sold and pushed about and have a cloth laid on it1 and so on1 cannot be a mere collection of sense-data4 ,if the cloth completely hides the table1 we shall derive no sense-data from the table1 and therefore1 if the table were merely sense-data1 it would have ceased to exist1 and the cloth would be suspended in empty air1 resting1 by a miracle1 in the place where the table formerly was4 ,this seems plainly absurd2 but whoever wishes to become a philosopher must learn not to be frightened by absurdities4 ,one great reason why it is felt that we must secure a physical object in addition to the sense-data1 is that we want the same object for different people4 ,when ten people are sitting round a dinner-table1 it seems preposterous to maintain that they are not seeing the same tablecloth1 the same knives and forks and spoons and glasses4 ,but the sense-data are private to each separate person2 what is immediately present to the sight of one is not immediately present to the sight of another3 they all see things from slightly different points of view1 and therefore see them slightly differently4 ,thus1 if there are to be public neutral objects1 which can be in some sense known to many different people1 there must be something over and above the private and particular sense-data which appear to various people4 ,what reason1 then1 have we for believing that there are such public neutral objects8 ,the first answer that naturally occurs to one is that1 although different people may see the table slightly differently1 still they all see more or less similar things when they look at the table1 and the variations in what they see follow the laws of perspective and reflection of light1 so that it is easy to arrive at a permanent object underlying all the different people's sense-data4 ,i bought my table from the former occupant of my room2 ,i could not buy his sense-data1 which died when he went away1 but ,i could and did buy the confident expectation of more or less similar sense-data4 ,thus it is the fact that different people have similar sense-data1 and that one person in a given place at different times has similar sense-data1 which makes us suppose that over and above the sense-data there is a permanent public object which underlies or causes the sense-data of various people at various times4 ,now in so far as the above considerations depend upon supposing that there are other people besides ourselves1 they beg the very question at issue4 ,other people are represented to me by certain sense-data1 such as the sight of them or the sound of their voices1 and if ,i had no reason to believe that there were physical objects independent of my sense-data1 ,i should have no reason to believe that other people exist except as part of my dream4 ,thus1 when we are trying to show that there must be objects independent of our own sense-data1 we cannot appeal to the testimony of other people1 since this testimony itself consists of sense-data1 and does not reveal other people's experiences unless our own sense-data are signs of things existing independently of us4 ,we must therefore1 if possible1 find1 in our own purely private experiences1 characteristics which show1 or tend to show1 that there are in the world things other than ourselves and our private experiences4 ,in one sense it must be admitted that we can never prove the existence of things other than ourselves and our experiences4 ,no logical absurdity results from the hypothesis that the world consists of myself and my thoughts and feelings and sensations1 and that everything else is mere fancy4 ,in dreams a very complicated world may seem to be present1 and yet on waking we find it was a delusion2 that is to say1 we find that the sense-data in the dream do not appear to have corresponded with such physical objects as we should naturally infer from our sense-data4 7,it is true that1 when the physical world is assumed1 it is possible to find physical causes for the sense-data in dreams3 a door banging1 for instance1 may cause us to dream of a naval engagement4 ,but although1 in this case1 there is a physical cause for the sense-data1 there is not a physical object corresponding to the sense-data in the way in which an actual naval battle would correspond47 ,there is no logical impossibility in the supposition that the whole of life is a dream1 in which we ourselves create all the objects that come before us4 ,but although this is not logically impossible1 there is no reason whatever to suppose that it is true2 and it is1 in fact1 a less simple hypothesis1 viewed as a means of accounting for the facts of our own life1 than the common-sense hypothesis that there really are objects independent of us1 whose action on us causes our sensations4 ,the way in which simplicity comes in from supposing that there really are physical objects is easily seen4 ,if the cat appears at one moment in one part of the room1 and at another in another part1 it is natural to suppose that it has moved from the one to the other1 passing over a series of intermediate positions4 ,but if it is merely a set of sense-data1 it cannot have ever been in any place where ,i did not see it2 thus we shall have to suppose that it did not exist at all while ,i was not looking1 but suddenly sprang into being in a new place4 ,if the cat exists whether ,i see it or not1 we can understand from our own experience how it gets hungry between one meal and the next2 but if it does not exist when ,i am not seeing it1 it seems odd that appetite should grow during non-existence as fast as during existence4 ,and if the cat consists only of sense-data1 it cannot be hungry1 since no hunger but my own can be a sense-datum to me4 ,thus the behaviour of the sense-data which represent the cat to me1 though it seems quite natural when regarded as an expression of hunger1 becomes utterly inexplicable when regarded as mere movements and changes of patches of colour1 which are as incapable of hunger as a triangle is of playing football4 ,but the difficulty in the case of the cat is nothing compared to the difficulty in the case of human beings4 ,when human beings speak--that is1 when we hear certain noises which we associate with ideas1 and simultaneously see certain motions of lips and expressions of face--it is very difficult to suppose that what we hear is not the expression of a thought1 as we know it would be if we emitted the same sounds4 ,of course similar things happen in dreams1 where we are mistaken as to the existence of other people4 ,but dreams are more or less suggested by what we call waking life1 and are capable of being more or less accounted for on scientific principles if we assume that there really is a physical world4 ,thus every principle of simplicity urges us to adopt the natural view1 that there really are objects other than ourselves and our sense-data which have an existence not dependent upon our perceiving them4 ,of course it is not by argument that we originally come by our belief in an independent external world4 ,we find this belief ready in ourselves as soon as we begin to reflect3 it is what may be called an instinctive belief4 ,we should never have been led to question this belief but for the fact that1 at any rate in the case of sight1 it seems as if the sense-datum itself were instinctively believed to be the independent object1 whereas argument shows that the object cannot be identical with the sense-datum4 ,this discovery1 however--which is not at all paradoxical in the case of taste and smell and sound1 and only slightly so in the case of touch--leaves undiminished our instinctive belief that there are objects corresponding to our sense-data4 ,since this belief does not lead to any difficulties1 but on the contrary tends to simplify and systematize our account of our experiences1 there seems no good reason for rejecting it4 ,we may therefore admit--though with a slight doubt derived from dreams--that the external world does really exist1 and is not wholly dependent for its existence upon our continuing to perceive it4 ,the argument which has led us to this conclusion is doubtless less strong than we could wish1 but it is typical of many philosophical arguments1 and it is therefore worth while to consider briefly its general character and validity4 ,all knowledge1 we find1 must be built up upon our instinctive beliefs1 and if these are rejected1 nothing is left4 ,but among our instinctive beliefs some are much stronger than others1 while many have1 by habit and association1 become entangled with other beliefs1 not really instinctive1 but falsely supposed to be part of what is believed instinctively4 ,philosophy should show us the hierarchy of our instinctive beliefs1 beginning with those we hold most strongly1 and presenting each as much isolated and as free from irrelevant additions as possible4 ,it should take care to show that1 in the form in which they are finally set forth1 our instinctive beliefs do not clash1 but form a harmonious system4 ,there can never be any reason for rejecting one instinctive belief except that it clashes with others2 thus1 if they are found to harmonize1 the whole system becomes worthy of acceptance4 ,it is of course possible that all or any of our beliefs may be mistaken1 and therefore all ought to be held with at least some slight element of doubt4 ,but we cannot have reason to reject a belief except on the ground of some other belief4 ,hence1 by organizing our instinctive beliefs and their consequences1 by considering which among them is most possible1 if necessary1 to modify or abandon1 we can arrive1 on the basis of accepting as our sole data what we instinctively believe1 at an orderly systematic organization of our knowledge1 in which1 though the possibility of error remains1 its likelihood is diminished by the interrelation of the parts and by the critical scrutiny which has preceded acquiescence4 ,this function1 at least1 philosophy can perform4 ,most philosophers1 rightly or wrongly1 believe that philosophy can do much more than this--that it can give us knowledge1 not otherwise attainable1 concerning the universe as a whole1 and concerning the nature of ultimate reality4 ,whether this be the case or not1 the more modest function we have spoken of can certainly be performed by philosophy1 and certainly suffices1 for those who have once begun to doubt the adequacy of common sense1 to justify the arduous and difficult labours that philosophical problems involve4 ,,chapter ,,iii4 ,,the ,,nature ,,of ,,matter ,in the preceding chapter we agreed1 though without being able to find demonstrative reasons1 that it is rational to believe that our sense-data--for example1 those which we regard as associated with my table--are really signs of the existence of something independent of us and our perceptions4 ,that is to say1 over and above the sensations of colour1 hardness1 noise1 and so on1 which make up the appearance of the table to me1 ,i assume that there is something else1 of which these things are appearances4 ,the colour ceases to exist if ,i shut my eyes1 the sensation of hardness ceases to exist if ,i remove my arm from contact with the table1 the sound ceases to exist if ,i cease to rap the table with my knuckles4 ,but ,i do not believe that when all these things cease the table ceases4 ,on the contrary1 ,i believe that it is because the table exists continuously that all these sense-data will reappear when ,i open my eyes1 replace my arm1 and begin again to rap with my knuckles4 ,the question we have to consider in this chapter is3 ,what is the nature of this real table1 which persists independently of my perception of it8 ,to this question physical science gives an answer1 somewhat incomplete it is true1 and in part still very hypothetical1 but yet deserving of respect so far as it goes4 ,physical science1 more or less unconsciously1 has drifted into the view that all natural phenomena ought to be reduced to motions4 ,light and heat and sound are all due to wave-motions1 which travel from the body emitting them to the person who sees light or feels heat or hears sound4 ,that which has the wave-motion is either aether or 'gross matter'1 but in either case is what the philosopher would call matter4 ,the only properties which science assigns to it are position in space1 and the power of motion according to the laws of motion4 ,science does not deny that it may have other properties2 but if so1 such other properties are not useful to the man of science1 and in no way assist him in explaining the phenomena4 ,it is sometimes said that 'light is a form of wave-motion'1 but this is misleading1 for the light which we immediately see1 which we know directly by means of our senses1 is not a form of wave-motion1 but something quite different--something which we all know if we are not blind1 though we cannot describe it so as to convey our knowledge to a man who is blind4 ,a wave-motion1 on the contrary1 could quite well be described to a blind man1 since he can acquire a knowledge of space by the sense of touch2 and he can experience a wave-motion by a sea voyage almost as well as we can4 ,but this1 which a blind man can understand1 is not what we mean by light3 we mean by light just that which a blind man can never understand1 and which we can never describe to him4 ,now this something1 which all of us who are not blind know1 is not1 according to science1 really to be found in the outer world3 it is something caused by the action of certain waves upon the eyes and nerves and brain of the person who sees the light4 ,when it is said that light is waves1 what is really meant is that waves are the physical cause of our sensations of light4 ,but light itself1 the thing which seeing people experience and blind people do not1 is not supposed by science to form any part of the world that is independent of us and our senses4 ,and very similar remarks would apply to other kinds of sensations4 ,it is not only colours and sounds and so on that are absent from the scientific world of matter1 but also space as we get it through sight or touch4 ,it is essential to science that its matter should be in a space1 but the space in which it is cannot be exactly the space we see or feel4 ,to begin with1 space as we see it is not the same as space as we get it by the sense of touch2 it is only by experience in infancy that we learn how to touch things we see1 or how to get a sight of things which we feel touching us4 ,but the space of science is neutral as between touch and sight2 thus it cannot be either the space of touch or the space of sight4 ,again1 different people see the same object as of different shapes1 according to their point of view4 ,a circular coin1 for example1 though we should always judge it to be circular1 will look oval unless we are straight in front of it4 ,when we judge that it is circular1 we are judging that it has a real shape which is not its apparent shape1 but belongs to it intrinsically apart from its appearance4 ,but this real shape1 which is what concerns science1 must be in a real space1 not the same as anybody's apparent space4 ,the real space is public1 the apparent space is private to the percipient4 ,in different people's private spaces the same object seems to have different shapes2 thus the real space1 in which it has its real shape1 must be different from the private spaces4 ,the space of science1 therefore1 though connected with the spaces we see and feel1 is not identical with them1 and the manner of its connexion requires investigation4 ,we agreed provisionally that physical objects cannot be quite like our sense-data1 but may be regarded as causing our sensations4 ,these physical objects are in the space of science1 which we may call 'physical' space4 ,it is important to notice that1 if our sensations are to be caused by physical objects1 there must be a physical space containing these objects and our sense-organs and nerves and brain4 ,we get a sensation of touch from an object when we are in contact with it2 that is to say1 when some part of our body occupies a place in physical space quite close to the space occupied by the object4 ,we see an object 7roughly speaking7 when no opaque body is between the object and our eyes in physical space4 ,similarly1 we only hear or smell or taste an object when we are sufficiently near to it1 or when it touches the tongue1 or has some suitable position in physical space relatively to our body4 ,we cannot begin to state what different sensations we shall derive from a given object under different circumstances unless we regard the object and our body as both in one physical space1 for it is mainly the relative positions of the object and our body that determine what sensations we shall derive from the object4 ,now our sense-data are situated in our private spaces1 either the space of sight or the space of touch or such vaguer spaces as other senses may give us4 ,if1 as science and common sense assume1 there is one public all-embracing physical space in which physical objects are1 the relative positions of physical objects in physical space must more or less correspond to the relative positions of sense-data in our private spaces4 ,there is no difficulty in supposing this to be the case4 ,if we see on a road one house nearer to us than another1 our other senses will bear out the view that it is nearer2 for example1 it will be reached sooner if we walk along the road4 ,other people will agree that the house which looks nearer to us is nearer2 the ordnance map will take the same view2 and thus everything points to a spatial relation between the houses corresponding to the relation between the sense-data which we see when we look at the houses4 ,thus we may assume that there is a physical space in which physical objects have spatial relations corresponding to those which the corresponding sense-data have in our private spaces4 ,it is this physical space which is dealt with in geometry and assumed in physics and astronomy4 ,assuming that there is physical space1 and that it does thus correspond to private spaces1 what can we know about it8 ,we can know only what is required in order to secure the correspondence4 ,that is to say1 we can know nothing of what it is like in itself1 but we can know the sort of arrangement of physical objects which results from their spatial relations4 ,we can know1 for example1 that the earth and moon and sun are in one straight line during an eclipse1 though we cannot know what a physical straight line is in itself1 as we know the look of a straight line in our visual space4 ,thus we come to know much more about the relations of distances in physical space than about the distances themselves2 we may know that one distance is greater than another1 or that it is along the same straight line as the other1 but we cannot have that immediate acquaintance with physical distances that we have with distances in our private spaces1 or with colours or sounds or other sense-data4 ,we can know all those things about physical space which a man born blind might know through other people about the space of sight2 but the kind of things which a man born blind could never know about the space of sight we also cannot know about physical space4 ,we can know the properties of the relations required to preserve the correspondence with sense-data1 but we cannot know the nature of the terms between which the relations hold4 ,with regard to time1 our feeling of duration or of the lapse of time is notoriously an unsafe guide as to the time that has elapsed by the clock4 ,times when we are bored or suffering pain pass slowly1 times when we are agreeably occupied pass quickly1 and times when we are sleeping pass almost as if they did not exist4 ,thus1 in so far as time is constituted by duration1 there is the same necessity for distinguishing a public and a private time as there was in the case of space4 ,but in so far as time consists in an order of before and after1 there is no need to make such a distinction2 the time-order which events seem to have is1 so far as we can see1 the same as the time-order which they do have4 ,at any rate no reason can be given for supposing that the two orders are not the same4 ,the same is usually true of space3 if a regiment of men are marching along a road1 the shape of the regiment will look different from different points of view1 but the men will appear arranged in the same order from all points of view4 ,hence we regard the order as true also in physical space1 whereas the shape is only supposed to correspond to the physical space so far as is required for the preservation of the order4 ,in saying that the time-order which events seem to have is the same as the time-order which they really have1 it is necessary to guard against a possible misunderstanding4 ,it must not be supposed that the various states of different physical objects have the same time-order as the sense-data which constitute the perceptions of those objects4 ,considered as physical objects1 the thunder and lightning are simultaneous2 that is to say1 the lightning is simultaneous with the disturbance of the air in the place where the disturbance begins1 namely1 where the lightning is4 ,but the sense-datum which we call hearing the thunder does not take place until the disturbance of the air has travelled as far as to where we are4 ,similarly1 it takes about eight minutes for the sun's light to reach us2 thus1 when we see the sun we are seeing the sun of eight minutes ago4 ,so far as our sense-data afford evidence as to the physical sun they afford evidence as to the physical sun of eight minutes ago2 if the physical sun had ceased to exist within the last eight minutes1 that would make no difference to the sense-data which we call 'seeing the sun'4 ,this affords a fresh illustration of the necessity of distinguishing between sense-data and physical objects4 ,what we have found as regards space is much the same as what we find in relation to the correspondence of the sense-data with their physical counterparts4 ,if one object looks blue and another red1 we may reasonably presume that there is some corresponding difference between the physical objects2 if two objects both look blue1 we may presume a corresponding similarity4 ,but we cannot hope to be acquainted directly with the quality in the physical object which makes it look blue or red4 ,science tells us that this quality is a certain sort of wave-motion1 and this sounds familiar1 because we think of wave-motions in the space we see4 ,but the wave-motions must really be in physical space1 with which we have no direct acquaintance2 thus the real wave-motions have not that familiarity which we might have supposed them to have4 ,and what holds for colours is closely similar to what holds for other sense-data4 ,thus we find that1 although the relations of physical objects have all sorts of knowable properties1 derived from their correspondence with the relations of sense-data1 the physical objects themselves remain unknown in their intrinsic nature1 so far at least as can be discovered by means of the senses4 ,the question remains whether there is any other method of discovering the intrinsic nature of physical objects4 ,the most natural1 though not ultimately the most defensible1 hypothesis to adopt in the first instance1 at any rate as regards visual sense-data1 would be that1 though physical objects cannot1 for the reasons we have been considering1 be exactly like sense-data1 yet they may be more or less like4 ,according to this view1 physical objects will1 for example1 really have colours1 and we might1 by good luck1 see an object as of the colour it really is4 ,the colour which an object seems to have at any given moment will in general be very similar1 though not quite the same1 from many different points of view2 we might thus suppose the 'real' colour to be a sort of medium colour1 intermediate between the various shades which appear from the different points of view4 ,such a theory is perhaps not capable of being definitely refuted1 but it can be shown to be groundless4 ,to begin with1 it is plain that the colour we see depends only upon the nature of the light-waves that strike the eye1 and is therefore modified by the medium intervening between us and the object1 as well as by the manner in which light is reflected from the object in the direction of the eye4 ,the intervening air alters colours unless it is perfectly clear1 and any strong reflection will alter them completely4 ,thus the colour we see is a result of the ray as it reaches the eye1 and not simply a property of the object from which the ray comes4 ,hence1 also1 provided certain waves reach the eye1 we shall see a certain colour1 whether the object from which the waves start has any colour or not4 ,thus it is quite gratuitous to suppose that physical objects have colours1 and therefore there is no justification for making such a supposition4 ,exactly similar arguments will apply to other sense-data4 ,it remains to ask whether there are any general philosophical arguments enabling us to say that1 if matter is real1 it must be of such and such a nature4 ,as explained above1 very many philosophers1 perhaps most1 have held that whatever is real must be in some sense mental1 or at any rate that whatever we can know anything about must be in some sense mental4 ,such philosophers are called 'idealists'4 ,idealists tell us that what appears as matter is really something mental2 namely1 either 7as ,leibniz held7 more or less rudimentary minds1 or 7as ,berkeley contended7 ideas in the minds which1 as we should commonly say1 'perceive' the matter4 ,thus idealists deny the existence of matter as something intrinsically different from mind1 though they do not deny that our sense-data are signs of something which exists independently of our private sensations4 ,in the following chapter we shall consider briefly the reasons--in my opinion fallacious--which idealists advance in favour of their theory4 ,,chapter ,,iv4 ,,idealism ,the word 'idealism' is used by different philosophers in somewhat different senses4 ,we shall understand by it the doctrine that whatever exists1 or at any rate whatever can be known to exist1 must be in some sense mental4 ,this doctrine1 which is very widely held among philosophers1 has several forms1 and is advocated on several different grounds4 ,the doctrine is so widely held1 and so interesting in itself1 that even the briefest survey of philosophy must give some account of it4 ,those who are unaccustomed to philosophical speculation may be inclined to dismiss such a doctrine as obviously absurd4 ,there is no doubt that common sense regards tables and chairs and the sun and moon and material objects generally as something radically different from minds and the contents of minds1 and as having an existence which might continue if minds ceased4 ,we think of matter as having existed long before there were any minds1 and it is hard to think of it as a mere product of mental activity4 ,but whether true or false1 idealism is not to be dismissed as obviously absurd4 ,we have seen that1 even if physical objects do have an independent existence1 they must differ very widely from sense-data1 and can only have a correspondence with sense-data1 in the same sort of way in which a catalogue has a correspondence with the things catalogued4 ,hence common sense leaves us completely in the dark as to the true intrinsic nature of physical objects1 and if there were good reason to regard them as mental1 we could not legitimately reject this opinion merely because it strikes us as strange4 ,the truth about physical objects must be strange4 ,it may be unattainable1 but if any philosopher believes that he has attained it1 the fact that what he offers as the truth is strange ought not to be made a ground of objection to his opinion4 ,the grounds on which idealism is advocated are generally grounds derived from the theory of knowledge1 that is to say1 from a discussion of the conditions which things must satisfy in order that we may be able to know them4 ,the first serious attempt to establish idealism on such grounds was that of ,bishop ,berkeley4 ,he proved first1 by arguments which were largely valid1 that our sense-data cannot be supposed to have an existence independent of us1 but must be1 in part at least1 'in' the mind1 in the sense that their existence would not continue if there were no seeing or hearing or touching or smelling or tasting4 ,so far1 his contention was almost certainly valid1 even if some of his arguments were not so4 ,but he went on to argue that sense-data were the only things of whose existence our perceptions could assure us2 and that to be known is to be 'in' a mind1 and therefore to be mental4 ,hence he concluded that nothing can ever be known except what is in some mind1 and that whatever is known without being in my mind must be in some other mind4 ,in order to understand his argument1 it is necessary to understand his use of the word 'idea'4 ,he gives the name 'idea' to anything which is immediately known1 as1 for example1 sense-data are known4 ,thus a particular colour which we see is an idea2 so is a voice which we hear1 and so on4 ,but the term is not wholly confined to sense-data4 ,there will also be things remembered or imagined1 for with such things also we have immediate acquaintance at the moment of remembering or imagining4 ,all such immediate data he calls 'ideas'4 ,he then proceeds to consider common objects1 such as a tree1 for instance4 ,he shows that all we know immediately when we 'perceive' the tree consists of ideas in his sense of the word1 and he argues that there is not the slightest ground for supposing that there is anything real about the tree except what is perceived4 ,its being1 he says1 consists in being perceived3 in the ,latin of the schoolmen its 'esse' is 'percipi'4 ,he fully admits that the tree must continue to exist even when we shut our eyes or when no human being is near it4 ,but this continued existence1 he says1 is due to the fact that ,god continues to perceive it2 the 'real' tree1 which corresponds to what we called the physical object1 consists of ideas in the mind of ,god1 ideas more or less like those we have when we see the tree1 but differing in the fact that they are permanent in ,god's mind so long as the tree continues to exist4 ,all our perceptions1 according to him1 consist in a partial participation in ,god's perceptions1 and it is because of this participation that different people see more or less the same tree4 ,thus apart from minds and their ideas there is nothing in the world1 nor is it possible that anything else should ever be known1 since whatever is known is necessarily an idea4 ,there are in this argument a good many fallacies which have been important in the history of philosophy1 and which it will be as well to bring to light4 ,in the first place1 there is a confusion engendered by the use of the word 'idea'4 ,we think of an idea as essentially something in somebody's mind1 and thus when we are told that a tree consists entirely of ideas1 it is natural to suppose that1 if so1 the tree must be entirely in minds4 ,but the notion of being 'in' the mind is ambiguous4 ,we speak of bearing a person in mind1 not meaning that the person is in our minds1 but that a thought of him is in our minds4 ,when a man says that some business he had to arrange went clean out of his mind1 he does not mean to imply that the business itself was ever in his mind1 but only that a thought of the business was formerly in his mind1 but afterwards ceased to be in his mind4 ,and so when ,berkeley says that the tree must be in our minds if we can know it1 all that he really has a right to say is that a thought of the tree must be in our minds4 ,to argue that the tree itself must be in our minds is like arguing that a person whom we bear in mind is himself in our minds4 ,this confusion may seem too gross to have been really committed by any competent philosopher1 but various attendant circumstances rendered it possible4 ,in order to see how it was possible1 we must go more deeply into the question as to the nature of ideas4 ,before taking up the general question of the nature of ideas1 we must disentangle two entirely separate questions which arise concerning sense-data and physical objects4 ,we saw that1 for various reasons of detail1 ,berkeley was right in treating the sense-data which constitute our perception of the tree as more or less subjective1 in the sense that they depend upon us as much as upon the tree1 and would not exist if the tree were not being perceived4 ,but this is an entirely different point from the one by which ,berkeley seeks to prove that whatever can be immediately known must be in a mind4 ,for this purpose arguments of detail as to the dependence of sense-data upon us are useless4 ,it is necessary to prove1 generally1 that by being known1 things are shown to be mental4 ,this is what ,berkeley believes himself to have done4 ,it is this question1 and not our previous question as to the difference between sense-data and the physical object1 that must now concern us4 ,taking the word 'idea' in ,berkeley's sense1 there are two quite distinct things to be considered whenever an idea is before the mind4 ,there is on the one hand the thing of which we are aware--say the colour of my table--and on the other hand the actual awareness itself1 the mental act of apprehending the thing4 ,the mental act is undoubtedly mental1 but is there any reason to suppose that the thing apprehended is in any sense mental8 ,our previous arguments concerning the colour did not prove it to be mental2 they only proved that its existence depends upon the relation of our sense organs to the physical object--in our case1 the table4 ,that is to say1 they proved that a certain colour will exist1 in a certain light1 if a normal eye is placed at a certain point relatively to the table4 ,they did not prove that the colour is in the mind of the percipient4 ,berkeley's view1 that obviously the colour must be in the mind1 seems to depend for its plausibility upon confusing the thing apprehended with the act of apprehension4 ,either of these might be called an 'idea'2 probably either would have been called an idea by ,berkeley4 ,the act is undoubtedly in the mind2 hence1 when we are thinking of the act1 we readily assent to the view that ideas must be in the mind4 ,then1 forgetting that this was only true when ideas were taken as acts of apprehension1 we transfer the proposition that 'ideas are in the mind' to ideas in the other sense1 i4e4 to the things apprehended by our acts of apprehension4 ,thus1 by an unconscious equivocation1 we arrive at the conclusion that whatever we can apprehend must be in our minds4 ,this seems to be the true analysis of ,berkeley's argument1 and the ultimate fallacy upon which it rests4 ,this question of the distinction between act and object in our apprehending of things is vitally important1 since our whole power of acquiring knowledge is bound up with it4 ,the faculty of being acquainted with things other than itself is the main characteristic of a mind4 ,acquaintance with objects essentially consists in a relation between the mind and something other than the mind2 it is this that constitutes the mind's power of knowing things4 ,if we say that the things known must be in the mind1 we are either unduly limiting the mind's power of knowing1 or we are uttering a mere tautology4 ,we are uttering a mere tautology if we mean by 'in the mind' the same as by 'before the mind'1 i4e4 if we mean merely being apprehended by the mind4 ,but if we mean this1 we shall have to admit that what1 in this sense1 is in the mind1 may nevertheless be not mental4 ,thus when we realize the nature of knowledge1 ,berkeley's argument is seen to be wrong in substance as well as in form1 and his grounds for supposing that 'ideas'--i4e4 the objects apprehended--must be mental1 are found to have no validity whatever4 ,hence his grounds in favour of idealism may be dismissed4 ,it remains to see whether there are any other grounds4 ,it is often said1 as though it were a self-evident truism1 that we cannot know that anything exists which we do not know4 ,it is inferred that whatever can in any way be relevant to our experience must be at least capable of being known by us2 whence it follows that if matter were essentially something with which we could not become acquainted1 matter would be something which we could not know to exist1 and which could have for us no importance whatever4 ,it is generally also implied1 for reasons which remain obscure1 that what can have no importance for us cannot be real1 and that therefore matter1 if it is not composed of minds or of mental ideas1 is impossible and a mere chimaera4 ,to go into this argument fully at our present stage would be impossible1 since it raises points requiring a considerable preliminary discussion2 but certain reasons for rejecting the argument may be noticed at once4 ,to begin at the end3 there is no reason why what cannot have any practical importance for us should not be real4 ,it is true that1 if theoretical importance is included1 everything real is of some importance to us1 since1 as persons desirous of knowing the truth about the universe1 we have some interest in everything that the universe contains4 ,but if this sort of interest is included1 it is not the case that matter has no importance for us1 provided it exists even if we cannot know that it exists4 ,we can1 obviously1 suspect that it may exist1 and wonder whether it does2 hence it is connected with our desire for knowledge1 and has the importance of either satisfying or thwarting this desire4 ,again1 it is by no means a truism1 and is in fact false1 that we cannot know that anything exists which we do not know4 ,the word 'know' is here used in two different senses4 7#a7 ,in its first use it is applicable to the sort of knowledge which is opposed to error1 the sense in which what we know is true1 the sense which applies to our beliefs and convictions1 i4e4 to what are called judgements4 ,in this sense of the word we know that something is the case4 ,this sort of knowledge may be described as knowledge of truths4 7#b7 ,in the second use of the word 'know' above1 the word applies to our knowledge of things1 which we may call acquaintance4 ,this is the sense in which we know sense-data4 7,the distinction involved is roughly that between savoir and connatre in ,french1 or between wissen and kennen in ,german47 ,thus the statement which seemed like a truism becomes1 when re-stated1 the following3 ',we can never truly judge that something with which we are not acquainted exists4' ,this is by no means a truism1 but on the contrary a palpable falsehood4 ,i have not the honour to be acquainted with the ,emperor of ,china1 but ,i truly judge that he exists4 ,it may be said1 of course1 that ,i judge this because of other people's acquaintance with him4 ,this1 however1 would be an irrelevant retort1 since1 if the principle were true1 ,i could not know that any one else is acquainted with him4 ,but further3 there is no reason why ,i should not know of the existence of something with which nobody is acquainted4 ,this point is important1 and demands elucidation4 ,if ,i am acquainted with a thing which exists1 my acquaintance gives me the knowledge that it exists4 ,but it is not true that1 conversely1 whenever ,i can know that a thing of a certain sort exists1 ,i or some one else must be acquainted with the thing4 ,what happens1 in cases where ,i have true judgement without acquaintance1 is that the thing is known to me by description1 and that1 in virtue of some general principle1 the existence of a thing answering to this description can be inferred from the existence of something with which ,i am acquainted4 ,in order to understand this point fully1 it will be well first to deal with the difference between knowledge by acquaintance and knowledge by description1 and then to consider what knowledge of general principles1 if any1 has the same kind of certainty as our knowledge of the existence of our own experiences4 ,these subjects will be dealt with in the following chapters4 ,,chapter ,v4 ,,knowledge ,,by ,,acquaintance ,,and ,,knowledge ,,by ,,description ,in the preceding chapter we saw that there are two sorts of knowledge3 knowledge of things1 and knowledge of truths4 ,in this chapter we shall be concerned exclusively with knowledge of things1 of which in turn we shall have to distinguish two kinds4 ,knowledge of things1 when it is of the kind we call knowledge by acquaintance1 is essentially simpler than any knowledge of truths1 and logically independent of knowledge of truths1 though it would be rash to assume that human beings ever1 in fact1 have acquaintance with things without at the same time knowing some truth about them4 ,knowledge of things by description1 on the contrary1 always involves1 as we shall find in the course of the present chapter1 some knowledge of truths as its source and ground4 ,but first of all we must make clear what we mean by 'acquaintance' and what we mean by 'description'4 ,we shall say that we have acquaintance with anything of which we are directly aware1 without the intermediary of any process of inference or any knowledge of truths4 ,thus in the presence of my table ,i am acquainted with the sense-data that make up the appearance of my table--its colour1 shape1 hardness1 smoothness1 etc42 all these are things of which ,i am immediately conscious when ,i am seeing and touching my table4 ,the particular shade of colour that ,i am seeing may have many things said about it--,i may say that it is brown1 that it is rather dark1 and so on4 ,but such statements1 though they make me know truths about the colour1 do not make me know the colour itself any better than ,i did before so far as concerns knowledge of the colour itself1 as opposed to knowledge of truths about it1 ,i know the colour perfectly and completely when ,i see it1 and no further knowledge of it itself is even theoretically possible4 ,thus the sense-data which make up the appearance of my table are things with which ,i have acquaintance1 things immediately known to me just as they are4 ,my knowledge of the table as a physical object1 on the contrary1 is not direct knowledge4 ,such as it is1 it is obtained through acquaintance with the sense-data that make up the appearance of the table4 ,we have seen that it is possible1 without absurdity1 to doubt whether there is a table at all1 whereas it is not possible to doubt the sense-data4 ,my knowledge of the table is of the kind which we shall call 'knowledge by description'4 ,the table is 'the physical object which causes such-and-such sense-data'4 ,this describes the table by means of the sense-data4 ,in order to know anything at all about the table1 we must know truths connecting it with things with which we have acquaintance3 we must know that 'such-and-such sense-data are caused by a physical object'4 ,there is no state of mind in which we are directly aware of the table2 all our knowledge of the table is really knowledge of truths1 and the actual thing which is the table is not1 strictly speaking1 known to us at all4 ,we know a description1 and we know that there is just one object to which this description applies1 though the object itself is not directly known to us4 ,in such a case1 we say that our knowledge of the object is knowledge by description4 ,all our knowledge1 both knowledge of things and knowledge of truths1 rests upon acquaintance as its foundation4 ,it is therefore important to consider what kinds of things there are with which we have acquaintance4 ,sense-data1 as we have already seen1 are among the things with which we are acquainted2 in fact1 they supply the most obvious and striking example of knowledge by acquaintance4 ,but if they were the sole example1 our knowledge would be very much more restricted than it is4 ,we should only know what is now present to our senses3 we could not know anything about the past--not even that there was a past--nor could we know any truths about our sense-data1 for all knowledge of truths1 as we shall show1 demands acquaintance with things which are of an essentially different character from sense-data1 the things which are sometimes called 'abstract ideas'1 but which we shall call 'universals'4 ,we have therefore to consider acquaintance with other things besides sense-data if we are to obtain any tolerably adequate analysis of our knowledge4 ,the first extension beyond sense-data to be considered is acquaintance by memory4 ,it is obvious that we often remember what we have seen or heard or had otherwise present to our senses1 and that in such cases we are still immediately aware of what we remember1 in spite of the fact that it appears as past and not as present4 ,this immediate knowledge by memory is the source of all our knowledge concerning the past3 without it1 there could be no knowledge of the past by inference1 since we should never know that there was anything past to be inferred4 ,the next extension to be considered is acquaintance by introspection4 ,we are not only aware of things1 but we are often aware of being aware of them4 ,when ,i see the sun1 ,i am often aware of my seeing the sun2 thus 'my seeing the sun' is an object with which ,i have acquaintance4 ,when ,i desire food1 ,i may be aware of my desire for food2 thus 'my desiring food' is an object with which ,i am acquainted4 ,similarly we may be aware of our feeling pleasure or pain1 and generally of the events which happen in our minds4 ,this kind of acquaintance1 which may be called self-consciousness1 is the source of all our knowledge of mental things4 ,it is obvious that it is only what goes on in our own minds that can be thus known immediately4 ,what goes on in the minds of others is known to us through our perception of their bodies1 that is1 through the sense-data in us which are associated with their bodies4 ,but for our acquaintance with the contents of our own minds1 we should be unable to imagine the minds of others1 and therefore we could never arrive at the knowledge that they have minds4 ,it seems natural to suppose that self-consciousness is one of the things that distinguish men from animals3 animals1 we may suppose1 though they have acquaintance with sense-data1 never become aware of this acquaintance4 ,i do not mean that they doubt whether they exist1 but that they have never become conscious of the fact that they have sensations and feelings1 nor therefore of the fact that they1 the subjects of their sensations and feelings1 exist4 ,we have spoken of acquaintance with the contents of our minds as self-consciousness1 but it is not1 of course1 consciousness of our self3 it is consciousness of particular thoughts and feelings4 ,the question whether we are also acquainted with our bare selves1 as opposed to particular thoughts and feelings1 is a very difficult one1 upon which it would be rash to speak positively4 ,when we try to look into ourselves we always seem to come upon some particular thought or feeling1 and not upon the ',i' which has the thought or feeling4 ,nevertheless there are some reasons for thinking that we are acquainted with the ',i'1 though the acquaintance is hard to disentangle from other things4 ,to make clear what sort of reason there is1 let us consider for a moment what our acquaintance with particular thoughts really involves4 ,when ,i am acquainted with 'my seeing the sun'1 it seems plain that ,i am acquainted with two different things in relation to each other4 ,on the one hand there is the sense-datum which represents the sun to me1 on the other hand there is that which sees this sense-datum4 ,all acquaintance1 such as my acquaintance with the sense-datum which represents the sun1 seems obviously a relation between the person acquainted and the object with which the person is acquainted4 ,when a case of acquaintance is one with which ,i can be acquainted 7as ,i am acquainted with my acquaintance with the sense-datum representing the sun71 it is plain that the person acquainted is myself4 ,thus1 when ,i am acquainted with my seeing the sun1 the whole fact with which ,i am acquainted is ',self-acquainted-with-sense-datum'4 ,further1 we know the truth ',i am acquainted with this sense-datum'4 ,it is hard to see how we could know this truth1 or even understand what is meant by it1 unless we were acquainted with something which we call ',i'4 ,it does not seem necessary to suppose that we are acquainted with a more or less permanent person1 the same to-day as yesterday1 but it does seem as though we must be acquainted with that thing1 whatever its nature1 which sees the sun and has acquaintance with sense-data4 ,thus1 in some sense it would seem we must be acquainted with our ,selves as opposed to our particular experiences4 ,but the question is difficult1 and complicated arguments can be adduced on either side4 ,hence1 although acquaintance with ourselves seems probably to occur1 it is not wise to assert that it undoubtedly does occur4 ,we may therefore sum up as follows what has been said concerning acquaintance with things that exist4 ,we have acquaintance in sensation with the data of the outer senses1 and in introspection with the data of what may be called the inner sense--thoughts1 feelings1 desires1 etc42 we have acquaintance in memory with things which have been data either of the outer senses or of the inner sense4 ,further1 it is probable1 though not certain1 that we have acquaintance with ,self1 as that which is aware of things or has desires towards things4 ,in addition to our acquaintance with particular existing things1 we also have acquaintance with what we shall call universals1 that is to say1 general ideas1 such as whiteness1 diversity1 brotherhood1 and so on4 ,every complete sentence must contain at least one word which stands for a universal1 since all verbs have a meaning which is universal4 ,we shall return to universals later on1 in ,chapter ,,ix2 for the present1 it is only necessary to guard against the supposition that whatever we can be acquainted with must be something particular and existent4 ,awareness of universals is called conceiving1 and a universal of which we are aware is called a concept4 ,it will be seen that among the objects with which we are acquainted are not included physical objects 7as opposed to sense-data71 nor other people's minds4 ,these things are known to us by what ,i call 'knowledge by description'1 which we must now consider4 ,by a 'description' ,i mean any phrase of the form 'a so-and-so' or 'the so-and-so'4 ,a phrase of the form 'a so-and-so' ,i shall call an 'ambiguous' description2 a phrase of the form 'the so-and-so' 7in the singular7 ,i shall call a 'definite' description4 ,thus 'a man' is an ambiguous description1 and 'the man with the iron mask' is a definite description4 ,there are various problems connected with ambiguous descriptions1 but ,i pass them by1 since they do not directly concern the matter we are discussing1 which is the nature of our knowledge concerning objects in cases where we know that there is an object answering to a definite description1 though we are not acquainted with any such object4 ,this is a matter which is concerned exclusively with definite descriptions4 ,i shall therefore1 in the sequel1 speak simply of 'descriptions' when ,i mean 'definite descriptions'4 ,thus a description will mean any phrase of the form 'the so-and-so' in the singular4 ,we shall say that an object is 'known by description' when we know that it is 'the so-and-so'1 i4e4 when we know that there is one object1 and no more1 having a certain property2 and it will generally be implied that we do not have knowledge of the same object by acquaintance4 ,we know that the man with the iron mask existed1 and many propositions are known about him2 but we do not know who he was4 ,we know that the candidate who gets the most votes will be elected1 and in this case we are very likely also acquainted 7in the only sense in which one can be acquainted with some one else7 with the man who is1 in fact1 the candidate who will get most votes2 but we do not know which of the candidates he is1 i4e4 we do not know any proposition of the form ',a is the candidate who will get most votes' where ,a is one of the candidates by name4 ,we shall say that we have 'merely descriptive knowledge' of the so-and-so when1 although we know that the so-and-so exists1 and although we may possibly be acquainted with the object which is1 in fact1 the so-and-so1 yet we do not know any proposition 'a is the so-and-so'1 where a is something with which we are acquainted4 ,when we say 'the so-and-so exists'1 we mean that there is just one object which is the so-and-so4 ,the proposition 'a is the so-and-so' means that a has the property so-and-so1 and nothing else has4 ',mr4 ,a4 is the ,unionist candidate for this constituency' means ',mr4 ,a4 is a ,unionist candidate for this constituency1 and no one else is'4 ',the ,unionist candidate for this constituency exists' means 'some one is a ,unionist candidate for this constituency1 and no one else is'4 ,thus1 when we are acquainted with an object which is the so-and-so1 we know that the so-and-so exists2 but we may know that the so-and-so exists when we are not acquainted with any object which we know to be the so-and-so1 and even when we are not acquainted with any object which1 in fact1 is the so-and-so4 ,common words1 even proper names1 are usually really descriptions4 ,that is to say1 the thought in the mind of a person using a proper name correctly can generally only be expressed explicitly if we replace the proper name by a description4 ,moreover1 the description required to express the thought will vary for different people1 or for the same person at different times4 ,the only thing constant 7so long as the name is rightly used7 is the object to which the name applies4 ,but so long as this remains constant1 the particular description involved usually makes no difference to the truth or falsehood of the proposition in which the name appears4 ,let us take some illustrations4 ,suppose some statement made about ,bismarck4 ,assuming that there is such a thing as direct acquaintance with oneself1 ,bismarck himself might have used his name directly to designate the particular person with whom he was acquainted4 ,in this case1 if he made a judgement about himself1 he himself might be a constituent of the judgement4 ,here the proper name has the direct use which it always wishes to have1 as simply standing for a certain object1 and not for a description of the object4 ,but if a person who knew ,bismarck made a judgement about him1 the case is different4 ,what this person was acquainted with were certain sense-data which he connected 7rightly1 we will suppose7 with ,bismarck's body4 ,his body1 as a physical object1 and still more his mind1 were only known as the body and the mind connected with these sense-data4 ,that is1 they were known by description4 ,it is1 of course1 very much a matter of chance which characteristics of a man's appearance will come into a friend's mind when he thinks of him2 thus the description actually in the friend's mind is accidental4 ,the essential point is that he knows that the various descriptions all apply to the same entity1 in spite of not being acquainted with the entity in question4 ,when we1 who did not know ,bismarck1 make a judgement about him1 the description in our minds will probably be some more or less vague mass of historical knowledge--far more1 in most cases1 than is required to identify him4 ,but1 for the sake of illustration1 let us assume that we think of him as 'the first ,chancellor of the ,german ,empire'4 ,here all the words are abstract except ',german'4 ,the word ',german' will1 again1 have different meanings for different people4 ,to some it will recall travels in ,germany1 to some the look of ,germany on the map1 and so on4 ,but if we are to obtain a description which we know to be applicable1 we shall be compelled1 at some point1 to bring in a reference to a particular with which we are acquainted4 ,such reference is involved in any mention of past1 present1 and future 7as opposed to definite dates71 or of here and there1 or of what others have told us4 ,thus it would seem that1 in some way or other1 a description known to be applicable to a particular must involve some reference to a particular with which we are acquainted1 if our knowledge about the thing described is not to be merely what follows logically from the description4 ,for example1 'the most long-lived of men' is a description involving only universals1 which must apply to some man1 but we can make no judgements concerning this man which involve knowledge about him beyond what the description gives4 ,if1 however1 we say1 ',the first ,chancellor of the ,german ,empire was an astute diplomatist'1 we can only be assured of the truth of our judgement in virtue of something with which we are acquainted--usually a testimony heard or read4 ,apart from the information we convey to others1 apart from the fact about the actual ,bismarck1 which gives importance to our judgement1 the thought we really have contains the one or more particulars involved1 and otherwise consists wholly of concepts4 ,all names of places--,london1 ,england1 ,europe1 the ,earth1 the ,solar ,system--similarly involve1 when used1 descriptions which start from some one or more particulars with which we are acquainted4 ,i suspect that even the ,universe1 as considered by metaphysics1 involves such a connexion with particulars4 ,in logic1 on the contrary1 where we are concerned not merely with what does exist1 but with whatever might or could exist or be1 no reference to actual particulars is involved4 ,it would seem that1 when we make a statement about something only known by description1 we often intend to make our statement1 not in the form involving the description1 but about the actual thing described4 ,that is to say1 when we say anything about ,bismarck1 we should like1 if we could1 to make the judgement which ,bismarck alone can make1 namely1 the judgement of which he himself is a constituent4 ,in this we are necessarily defeated1 since the actual ,bismarck is unknown to us4 ,but we know that there is an object ,b1 called ,bismarck1 and that ,b was an astute diplomatist4 ,we can thus describe the proposition we should like to affirm1 namely1 ',b was an astute diplomatist'1 where ,b is the object which was ,bismarck4 ,if we are describing ,bismarck as 'the first ,chancellor of the ,german ,empire'1 the proposition we should like to affirm may be described as 'the proposition asserting1 concerning the actual object which was the first ,chancellor of the ,german ,empire1 that this object was an astute diplomatist'4 ,what enables us to communicate in spite of the varying descriptions we employ is that we know there is a true proposition concerning the actual ,bismarck1 and that however we may vary the description 7so long as the description is correct7 the proposition described is still the same4 ,this proposition1 which is described and is known to be true1 is what interests us2 but we are not acquainted with the proposition itself1 and do not know it1 though we know it is true4 ,it will be seen that there are various stages in the removal from acquaintance with particulars3 there is ,bismarck to people who knew him2 ,bismarck to those who only know of him through history2 the man with the iron mask2 the longest-lived of men4 ,these are progressively further removed from acquaintance with particulars2 the first comes as near to acquaintance as is possible in regard to another person2 in the second1 we shall still be said to know 'who ,bismarck was'2 in the third1 we do not know who was the man with the iron mask1 though we can know many propositions about him which are not logically deducible from the fact that he wore an iron mask2 in the fourth1 finally1 we know nothing beyond what is logically deducible from the definition of the man4 ,there is a similar hierarchy in the region of universals4 ,many universals1 like many particulars1 are only known to us by description4 ,but here1 as in the case of particulars1 knowledge concerning what is known by description is ultimately reducible to knowledge concerning what is known by acquaintance4 ,the fundamental principle in the analysis of propositions containing descriptions is this3 ,every proposition which we can understand must be composed wholly of constituents with which we are acquainted4 ,we shall not at this stage attempt to answer all the objections which may be urged against this fundamental principle4 ,for the present1 we shall merely point out that1 in some way or other1 it must be possible to meet these objections1 for it is scarcely conceivable that we can make a judgement or entertain a supposition without knowing what it is that we are judging or supposing about4 ,we must attach some meaning to the words we use1 if we are to speak significantly and not utter mere noise2 and the meaning we attach to our words must be something with which we are acquainted4 ,thus when1 for example1 we make a statement about ,julius ,caesar1 it is plain that ,julius ,caesar himself is not before our minds1 since we are not acquainted with him4 ,we have in mind some description of ,julius ,caesar3 'the man who was assassinated on the ,ides of ,march'1 'the founder of the ,roman ,empire'1 or1 perhaps1 merely 'the man whose name was ,julius ,caesar'4 7,in this last description1 ,julius ,caesar is a noise or shape with which we are acquainted47 ,thus our statement does not mean quite what it seems to mean1 but means something involving1 instead of ,julius ,caesar1 some description of him which is composed wholly of particulars and universals with which we are acquainted4 ,the chief importance of knowledge by description is that it enables us to pass beyond the limits of our private experience4 ,in spite of the fact that we can only know truths which are wholly composed of terms which we have experienced in acquaintance1 we can yet have knowledge by description of things which we have never experienced4 ,in view of the very narrow range of our immediate experience1 this result is vital1 and until it is understood1 much of our knowledge must remain mysterious and therefore doubtful4 ,,chapter ,,vi4 ,,on ,,induction ,in almost all our previous discussions we have been concerned in the attempt to get clear as to our data in the way of knowledge of existence4 ,what things are there in the universe whose existence is known to us owing to our being acquainted with them8 ,so far1 our answer has been that we are acquainted with our sense-data1 and1 probably1 with ourselves4 ,these we know to exist4 ,and past sense-data which are remembered are known to have existed in the past4 ,this knowledge supplies our data4 ,but if we are to be able to draw inferences from these data--if we are to know of the existence of matter1 of other people1 of the past before our individual memory begins1 or of the future1 we must know general principles of some kind by means of which such inferences can be drawn4 ,it must be known to us that the existence of some one sort of thing1 ,a1 is a sign of the existence of some other sort of thing1 ,b1 either at the same time as ,a or at some earlier or later time1 as1 for example1 thunder is a sign of the earlier existence of lightning4 ,if this were not known to us1 we could never extend our knowledge beyond the sphere of our private experience2 and this sphere1 as we have seen1 is exceedingly limited4 ,the question we have now to consider is whether such an extension is possible1 and if so1 how it is effected4 ,let us take as an illustration a matter about which none of us1 in fact1 feel the slightest doubt4 ,we are all convinced that the sun will rise to-morrow4 ,why8 ,is this belief a mere blind outcome of past experience1 or can it be justified as a reasonable belief8 ,it is not easy to find a test by which to judge whether a belief of this kind is reasonable or not1 but we can at least ascertain what sort of general beliefs would suffice1 if true1 to justify the judgement that the sun will rise to-morrow1 and the many other similar judgements upon which our actions are based4 ,it is obvious that if we are asked why we believe that the sun will rise to-morrow1 we shall naturally answer ',because it always has risen every day'4 ,we have a firm belief that it will rise in the future1 because it has risen in the past4 ,if we are challenged as to why we believe that it will continue to rise as heretofore1 we may appeal to the laws of motion3 the earth1 we shall say1 is a freely rotating body1 and such bodies do not cease to rotate unless something interferes from outside1 and there is nothing outside to interfere with the earth between now and to-morrow4 ,of course it might be doubted whether we are quite certain that there is nothing outside to interfere1 but this is not the interesting doubt4 ,the interesting doubt is as to whether the laws of motion will remain in operation until to-morrow4 ,if this doubt is raised1 we find ourselves in the same position as when the doubt about the sunrise was first raised4 ,the only reason for believing that the laws of motion will remain in operation is that they have operated hitherto1 so far as our knowledge of the past enables us to judge4 ,it is true that we have a greater body of evidence from the past in favour of the laws of motion than we have in favour of the sunrise1 because the sunrise is merely a particular case of fulfilment of the laws of motion1 and there are countless other particular cases4 ,but the real question is3 ,do any number of cases of a law being fulfilled in the past afford evidence that it will be fulfilled in the future8 ,if not1 it becomes plain that we have no ground whatever for expecting the sun to rise to-morrow1 or for expecting the bread we shall eat at our next meal not to poison us1 or for any of the other scarcely conscious expectations that control our daily lives4 ,it is to be observed that all such expectations are only probable2 thus we have not to seek for a proof that they must be fulfilled1 but only for some reason in favour of the view that they are likely to be fulfilled4 ,now in dealing with this question we must1 to begin with1 make an important distinction1 without which we should soon become involved in hopeless confusions4 ,experience has shown us that1 hitherto1 the frequent repetition of some uniform succession or coexistence has been a cause of our expecting the same succession or coexistence on the next occasion4 ,food that has a certain appearance generally has a certain taste1 and it is a severe shock to our expectations when the familiar appearance is found to be associated with an unusual taste4 ,things which we see become associated1 by habit1 with certain tactile sensations which we expect if we touch them2 one of the horrors of a ghost 7in many ghost-stories7 is that it fails to give us any sensations of touch4 ,uneducated people who go abroad for the first time are so surprised as to be incredulous when they find their native language not understood4 ,and this kind of association is not confined to men2 in animals also it is very strong4 ,a horse which has been often driven along a certain road resists the attempt to drive him in a different direction4 ,domestic animals expect food when they see the person who usually feeds them4 ,we know that all these rather crude expectations of uniformity are liable to be misleading4 ,the man who has fed the chicken every day throughout its life at last wrings its neck instead1 showing that more refined views as to the uniformity of nature would have been useful to the chicken4 ,but in spite of the misleadingness of such expectations1 they nevertheless exist4 ,the mere fact that something has happened a certain number of times causes animals and men to expect that it will happen again4 ,thus our instincts certainly cause us to believe that the sun will rise to-morrow1 but we may be in no better a position than the chicken which unexpectedly has its neck wrung4 ,we have therefore to distinguish the fact that past uniformities cause expectations as to the future1 from the question whether there is any reasonable ground for giving weight to such expectations after the question of their validity has been raised4 ,the problem we have to discuss is whether there is any reason for believing in what is called 'the uniformity of nature'4 ,the belief in the uniformity of nature is the belief that everything that has happened or will happen is an instance of some general law to which there are no exceptions4 ,the crude expectations which we have been considering are all subject to exceptions1 and therefore liable to disappoint those who entertain them4 ,but science habitually assumes1 at least as a working hypothesis1 that general rules which have exceptions can be replaced by general rules which have no exceptions4 ',unsupported bodies in air fall' is a general rule to which balloons and aeroplanes are exceptions4 ,but the laws of motion and the law of gravitation1 which account for the fact that most bodies fall1 also account for the fact that balloons and aeroplanes can rise2 thus the laws of motion and the law of gravitation are not subject to these exceptions4 ,the belief that the sun will rise to-morrow might be falsified if the earth came suddenly into contact with a large body which destroyed its rotation2 but the laws of motion and the law of gravitation would not be infringed by such an event4 ,the business of science is to find uniformities1 such as the laws of motion and the law of gravitation1 to which1 so far as our experience extends1 there are no exceptions4 ,in this search science has been remarkably successful1 and it may be conceded that such uniformities have held hitherto4 ,this brings us back to the question3 ,have we any reason1 assuming that they have always held in the past1 to suppose that they will hold in the future8 ,it has been argued that we have reason to know that the future will resemble the past1 because what was the future has constantly become the past1 and has always been found to resemble the past1 so that we really have experience of the future1 namely of times which were formerly future1 which we may call past futures4 ,but such an argument really begs the very question at issue4 ,we have experience of past futures1 but not of future futures1 and the question is3 ,will future futures resemble past futures8 ,this question is not to be answered by an argument which starts from past futures alone4 ,we have therefore still to seek for some principle which shall enable us to know that the future will follow the same laws as the past4 ,the reference to the future in this question is not essential4 ,the same question arises when we apply the laws that work in our experience to past things of which we have no experience--as1 for example1 in geology1 or in theories as to the origin of the ,solar ,system4 ,the question we really have to ask is3 ',when two things have been found to be often associated1 and no instance is known of the one occurring without the other1 does the occurrence of one of the two1 in a fresh instance1 give any good ground for expecting the other8' ,on our answer to this question must depend the validity of the whole of our expectations as to the future1 the whole of the results obtained by induction1 and in fact practically all the beliefs upon which our daily life is based4 ,it must be conceded1 to begin with1 that the fact that two things have been found often together and never apart does not1 by itself1 suffice to prove demonstratively that they will be found together in the next case we examine4 ,the most we can hope is that the oftener things are found together1 the more probable it becomes that they will be found together another time1 and that1 if they have been found together often enough1 the probability will amount almost to certainty4 ,it can never quite reach certainty1 because we know that in spite of frequent repetitions there sometimes is a failure at the last1 as in the case of the chicken whose neck is wrung4 ,thus probability is all we ought to seek4 ,it might be urged1 as against the view we are advocating1 that we know all natural phenomena to be subject to the reign of law1 and that sometimes1 on the basis of observation1 we can see that only one law can possibly fit the facts of the case4 ,now to this view there are two answers4 ,the first is that1 even if some law which has no exceptions applies to our case1 we can never1 in practice1 be sure that we have discovered that law and not one to which there are exceptions4 ,the second is that the reign of law would seem to be itself only probable1 and that our belief that it will hold in the future1 or in unexamined cases in the past1 is itself based upon the very principle we are examining4 ,the principle we are examining may be called the principle of induction1 and its two parts may be stated as follows3 7a7 ,when a thing of a certain sort ,a has been found to be associated with a thing of a certain other sort ,b1 and has never been found dissociated from a thing of the sort ,b1 the greater the number of cases in which ,a and ,b have been associated1 the greater is the probability that they will be associated in a fresh case in which one of them is known to be present2 7b7 ,under the same circumstances1 a sufficient number of cases of association will make the probability of a fresh association nearly a certainty1 and will make it approach certainty without limit4 ,as just stated1 the principle applies only to the verification of our expectation in a single fresh instance4 ,but we want also to know that there is a probability in favour of the general law that things of the sort ,a are always associated with things of the sort ,b1 provided a sufficient number of cases of association are known1 and no cases of failure of association are known4 ,the probability of the general law is obviously less than the probability of the particular case1 since if the general law is true1 the particular case must also be true1 whereas the particular case may be true without the general law being true4 ,nevertheless the probability of the general law is increased by repetitions1 just as the probability of the particular case is4 ,we may therefore repeat the two parts of our principle as regards the general law1 thus3 7a7 ,the greater the number of cases in which a thing of the sort ,a has been found associated with a thing of the sort ,b1 the more probable it is 7if no cases of failure of association are known7 that ,a is always associated with ,b2 b7 ,under the same circumstances1 a sufficient number of cases of the association of ,a with ,b will make it nearly certain that ,a is always associated with ,b1 and will make this general law approach certainty without limit4 ,it should be noted that probability is always relative to certain data4 ,in our case1 the data are merely the known cases of coexistence of ,a and ,b4 ,there may be other data1 which might be taken into account1 which would gravely alter the probability4 ,for example1 a man who had seen a great many white swans might argue1 by our principle1 that on the data it was probable that all swans were white1 and this might be a perfectly sound argument4 ,the argument is not disproved by the fact that some swans are black1 because a thing may very well happen in spite of the fact that some data render it improbable4 ,in the case of the swans1 a man might know that colour is a very variable characteristic in many species of animals1 and that1 therefore1 an induction as to colour is peculiarly liable to error4 ,but this knowledge would be a fresh datum1 by no means proving that the probability relatively to our previous data had been wrongly estimated4 ,the fact1 therefore1 that things often fail to fulfil our expectations is no evidence that our expectations will not probably be fulfilled in a given case or a given class of cases4 ,thus our inductive principle is at any rate not capable of being disproved by an appeal to experience4 ,the inductive principle1 however1 is equally incapable of being proved by an appeal to experience4 ,experience might conceivably confirm the inductive principle as regards the cases that have been already examined2 but as regards unexamined cases1 it is the inductive principle alone that can justify any inference from what has been examined to what has not been examined4 ,all arguments which1 on the basis of experience1 argue as to the future or the unexperienced parts of the past or present1 assume the inductive principle2 hence we can never use experience to prove the inductive principle without begging the question4 ,thus we must either accept the inductive principle on the ground of its intrinsic evidence1 or forgo all justification of our expectations about the future4 ,if the principle is unsound1 we have no reason to expect the sun to rise to-morrow1 to expect bread to be more nourishing than a stone1 or to expect that if we throw ourselves off the roof we shall fall4 ,when we see what looks like our best friend approaching us1 we shall have no reason to suppose that his body is not inhabited by the mind of our worst enemy or of some total stranger4 ,all our conduct is based upon associations which have worked in the past1 and which we therefore regard as likely to work in the future2 and this likelihood is dependent for its validity upon the inductive principle4 ,the general principles of science1 such as the belief in the reign of law1 and the belief that every event must have a cause1 are as completely dependent upon the inductive principle as are the beliefs of daily life ,all such general principles are believed because mankind have found innumerable instances of their truth and no instances of their falsehood4 ,but this affords no evidence for their truth in the future1 unless the inductive principle is assumed4 ,thus all knowledge which1 on a basis of experience tells us something about what is not experienced1 is based upon a belief which experience can neither confirm nor confute1 yet which1 at least in its more concrete applications1 appears to be as firmly rooted in us as many of the facts of experience4 ,the existence and justification of such beliefs--for the inductive principle1 as we shall see1 is not the only example--raises some of the most difficult and most debated problems of philosophy4 ,we will1 in the next chapter1 consider briefly what may be said to account for such knowledge1 and what is its scope and its degree of certainty4 ,,chapter ,,vii4 ,,on ,,our ,,knowledge ,,of ,,general ,,principles ,we saw in the preceding chapter that the principle of induction1 while necessary to the validity of all arguments based on experience1 is itself not capable of being proved by experience1 and yet is unhesitatingly believed by every one1 at least in all its concrete applications4 ,in these characteristics the principle of induction does not stand alone4 ,there are a number of other principles which cannot be proved or disproved by experience1 but are used in arguments which start from what is experienced4 ,some of these principles have even greater evidence than the principle of induction1 and the knowledge of them has the same degree of certainty as the knowledge of the existence of sense-data4 ,they constitute the means of drawing inferences from what is given in sensation2 and if what we infer is to be true1 it is just as necessary that our principles of inference should be true as it is that our data should be true4 ,the principles of inference are apt to be overlooked because of their very obviousness--the assumption involved is assented to without our realizing that it is an assumption4 ,but it is very important to realize the use of principles of inference1 if a correct theory of knowledge is to be obtained2 for our knowledge of them raises interesting and difficult questions4 ,in all our knowledge of general principles1 what actually happens is that first of all we realize some particular application of the principle1 and then we realize that the particularity is irrelevant1 and that there is a generality which may equally truly be affirmed4 ,this is of course familiar in such matters as teaching arithmetic3 'two and two are four' is first learnt in the case of some particular pair of couples1 and then in some other particular case1 and so on1 until at last it becomes possible to see that it is true of any pair of couples4 ,the same thing happens with logical principles4 ,suppose two men are discussing what day of the month it is4 ,one of them says1 ',at least you will admit that if yesterday was the #aeth to-day must be the #afth4' ',yes'1 says the other1 ',i admit that4' ',and you know'1 the first continues1 'that yesterday was the #aeth1 because you dined with ,jones1 and your diary will tell you that was on the #aeth4' ',yes'1 says the second2 'therefore to-day is the #afth4' ,now such an argument is not hard to follow2 and if it is granted that its premisses are true in fact1 no one will deny that the conclusion must also be true4 ,but it depends for its truth upon an instance of a general logical principle4 ,the logical principle is as follows3 ',suppose it known that if this is true1 then that is true4 ,suppose it also known that this is true1 then it follows that that is true4' ,when it is the case that if this is true1 that is true1 we shall say that this 'implies' that1 and that that 'follows from' this4 ,thus our principle states that if this implies that1 and this is true1 then that is true4 ,in other words1 'anything implied by a true proposition is true'1 or 'whatever follows from a true proposition is true'4 ,this principle is really involved--at least1 concrete instances of it are involved--in all demonstrations4 ,whenever one thing which we believe is used to prove something else1 which we consequently believe1 this principle is relevant4 ,if any one asks3 ',why should ,i accept the results of valid arguments based on true premisses8' we can only answer by appealing to our principle4 ,in fact1 the truth of the principle is impossible to doubt1 and its obviousness is so great that at first sight it seems almost trivial4 ,such principles1 however1 are not trivial to the philosopher1 for they show that we may have indubitable knowledge which is in no way derived from objects of sense4 ,the above principle is merely one of a certain number of self-evident logical principles4 ,some at least of these principles must be granted before any argument or proof becomes possible4 ,when some of them have been granted1 others can be proved1 though these others1 so long as they are simple1 are just as obvious as the principles taken for granted4 ,for no very good reason1 three of these principles have been singled out by tradition under the name of ',laws of ,thought'4 ,they are as follows3 7#a7 ,the law of identity3 ',whatever is1 is4' 7#b7 ,the law of contradiction3 ',nothing can both be and not be4' 7#c7 ,the law of excluded middle3 ',everything must either be or not be4' ,these three laws are samples of self-evident logical principles1 but are not really more fundamental or more self-evident than various other similar principles3 for instance1 the one we considered just now1 which states that what follows from a true premiss is true4 ,the name 'laws of thought' is also misleading1 for what is important is not the fact that we think in accordance with these laws1 but the fact that things behave in accordance with them2 in other words1 the fact that when we think in accordance with them we think truly4 ,but this is a large question1 to which we must return at a later stage4 ,in addition to the logical principles which enable us to prove from a given premiss that something is certainly true1 there are other logical principles which enable us to prove1 from a given premiss1 that there is a greater or less probability that something is true4 ,an example of such principles--perhaps the most important example is the inductive principle1 which we considered in the preceding chapter4 ,one of the great historic controversies in philosophy is the controversy between the two schools called respectively 'empiricists' and 'rationalists'4 ,the empiricists--who are best represented by the ,british philosophers1 ,locke1 ,berkeley1 and ,hume--maintained that all our knowledge is derived from experience2 the rationalists--who are represented by the ,continental philosophers of the seventeenth century1 especially ,descartes and ,leibniz--maintained that1 in addition to what we know by experience1 there are certain 'innate ideas' and 'innate principles'1 which we know independently of experience4 ,it has now become possible to decide with some confidence as to the truth or falsehood of these opposing schools4 ,it must be admitted1 for the reasons already stated1 that logical principles are known to us1 and cannot be themselves proved by experience1 since all proof presupposes them4 ,in this1 therefore1 which was the most important point of the controversy1 the rationalists were in the right4 ,on the other hand1 even that part of our knowledge which is logically independent of experience 7in the sense that experience cannot prove it7 is yet elicited and caused by experience4 ,it is on occasion of particular experiences that we become aware of the general laws which their connexions exemplify4 ,it would certainly be absurd to suppose that there are innate principles in the sense that babies are born with a knowledge of everything which men know and which cannot be deduced from what is experienced4 ,for this reason1 the word 'innate' would not now be employed to describe our knowledge of logical principles4 ,the phrase 'a priori' is less objectionable1 and is more usual in modern writers4 ,thus1 while admitting that all knowledge is elicited and caused by experience1 we shall nevertheless hold that some knowledge is a priori1 in the sense that the experience which makes us think of it does not suffice to prove it1 but merely so directs our attention that we see its truth without requiring any proof from experience4 ,there is another point of great importance1 in which the empiricists were in the right as against the rationalists4 ,nothing can be known to exist except by the help of experience4 ,that is to say1 if we wish to prove that something of which we have no direct experience exists1 we must have among our premisses the existence of one or more things of which we have direct experience4 ,our belief that the ,emperor of ,china exists1 for example1 rests upon testimony1 and testimony consists1 in the last analysis1 of sense-data seen or heard in reading or being spoken to4 ,rationalists believed that1 from general consideration as to what must be1 they could deduce the existence of this or that in the actual world4 ,in this belief they seem to have been mistaken4 ,all the knowledge that we can acquire a priori concerning existence seems to be hypothetical3 it tells us that if one thing exists1 another must exist1 or1 more generally1 that if one proposition is true1 another must be true4 ,this is exemplified by the principles we have already dealt with1 such as 'if this is true1 and this implies that1 then that is true'1 or 'if this and that have been repeatedly found connected1 they will probably be connected in the next instance in which one of them is found'4 ,thus the scope and power of a priori principles is strictly limited4 ,all knowledge that something exists must be in part dependent on experience4 ,when anything is known immediately1 its existence is known by experience alone2 when anything is proved to exist1 without being known immediately1 both experience and a priori principles must be required in the proof4 ,knowledge is called empirical when it rests wholly or partly upon experience4 ,thus all knowledge which asserts existence is empirical1 and the only a priori knowledge concerning existence is hypothetical1 giving connexions among things that exist or may exist1 but not giving actual existence4 ,a priori knowledge is not all of the logical kind we have been hitherto considering4 ,perhaps the most important example of non-logical a priori knowledge is knowledge as to ethical value4 ,i am not speaking of judgements as to what is useful or as to what is virtuous1 for such judgements do require empirical premisses2 ,i am speaking of judgements as to the intrinsic desirability of things4 ,if something is useful1 it must be useful because it secures some end2 the end must1 if we have gone far enough1 be valuable on its own account1 and not merely because it is useful for some further end4 ,thus all judgements as to what is useful depend upon judgements as to what has value on its own account4 ,we judge1 for example1 that happiness is more desirable than misery1 knowledge than ignorance1 goodwill than hatred1 and so on4 ,such judgements must1 in part at least1 be immediate and a priori4 ,like our previous a priori judgements1 they may be elicited by experience1 and indeed they must be2 for it seems not possible to judge whether anything is intrinsically valuable unless we have experienced something of the same kind4 ,but it is fairly obvious that they cannot be proved by experience2 for the fact that a thing exists or does not exist cannot prove either that it is good that it should exist or that it is bad4 ,the pursuit of this subject belongs to ethics1 where the impossibility of deducing what ought to be from what is has to be established4 ,in the present connexion1 it is only important to realize that knowledge as to what is intrinsically of value is a priori in the same sense in which logic is a priori1 namely in the sense that the truth of such knowledge can be neither proved nor disproved by experience4 ,all pure mathematics is a priori1 like logic4 ,this was strenuously denied by the empirical philosophers1 who maintained that experience was as much the source of our knowledge of arithmetic as of our knowledge of geography4 ,they maintained that by the repeated experience of seeing two things and two other things1 and finding that altogether they made four things1 we were led by induction to the conclusion that two things and two other things would always make four things altogether4 ,if1 however1 this were the source of our knowledge that two and two are four1 we should proceed differently1 in persuading ourselves of its truth1 from the way in which we do actually proceed4 ,in fact1 a certain number of instances are needed to make us think of two abstractly1 rather than of two coins or two books or two people1 or two of any other specified kind4 ,but as soon as we are able to divest our thoughts of irrelevant particularity1 we become able to see the general principle that two and two are four2 any one instance is seen to be typical1 and the examination of other instances becomes unnecessary47#a7 7#a7 ,cf4 ,a4 ,n4 ,whitehead1 ,introduction to ,mathematics 7,home ,university ,library74 ,the same thing is exemplified in geometry4 ,if we want to prove some property of all triangles1 we draw some one triangle and reason about it2 but we can avoid making use of any property which it does not share with all other triangles1 and thus1 from our particular case1 we obtain a general result4 ,we do not1 in fact1 feel our certainty that two and two are four increased by fresh instances1 because1 as soon as we have seen the truth of this proposition1 our certainty becomes so great as to be incapable of growing greater4 ,moreover1 we feel some quality of necessity about the proposition 'two and two are four'1 which is absent from even the best attested empirical generalizations4 ,such generalizations always remain mere facts3 we feel that there might be a world in which they were false1 though in the actual world they happen to be true4 ,in any possible world1 on the contrary1 we feel that two and two would be four3 this is not a mere fact1 but a necessity to which everything actual and possible must conform4 ,the case may be made clearer by considering a genuinely-empirical generalization1 such as ',all men are mortal4' ,it is plain that we believe this proposition1 in the first place1 because there is no known instance of men living beyond a certain age1 and in the second place because there seem to be physiological grounds for thinking that an organism such as a man's body must sooner or later wear out4 ,neglecting the second ground1 and considering merely our experience of men's mortality1 it is plain that we should not be content with one quite clearly understood instance of a man dying1 whereas1 in the case of 'two and two are four'1 one instance does suffice1 when carefully considered1 to persuade us that the same must happen in any other instance4 ,also we can be forced to admit1 on reflection1 that there may be some doubt1 however slight1 as to whether all men are mortal4 ,this may be made plain by the attempt to imagine two different worlds1 in one of which there are men who are not mortal1 while in the other two and two make five4 ,when ,swift invites us to consider the race of ,struldbugs who never die1 we are able to acquiesce in imagination4 ,but a world where two and two make five seems quite on a different level4 ,we feel that such a world1 if there were one1 would upset the whole fabric of our knowledge and reduce us to utter doubt4 ,the fact is that1 in simple mathematical judgements such as 'two and two are four'1 and also in many judgements of logic1 we can know the general proposition without inferring it from instances1 although some instance is usually necessary to make clear to us what the general proposition means4 ,this is why there is real utility in the process of deduction1 which goes from the general to the general1 or from the general to the particular1 as well as in the process of induction1 which goes from the particular to the particular1 or from the particular to the general4 ,it is an old debate among philosophers whether deduction ever gives new knowledge4 ,we can now see that in certain cases1 at least1 it does do so4 ,if we already know that two and two always make four1 and we know that ,brown and ,jones are two1 and so are ,robinson and ,smith1 we can deduce that ,brown and ,jones and ,robinson and ,smith are four4 ,this is new knowledge1 not contained in our premisses1 because the general proposition1 'two and two are four'1 never told us there were such people as ,brown and ,jones and ,robinson and ,smith1 and the particular premisses do not tell us that there were four of them1 whereas the particular proposition deduced does tell us both these things4 ,but the newness of the knowledge is much less certain if we take the stock instance of deduction that is always given in books on logic1 namely1 ',all men are mortal2 ,socrates is a man1 therefore ,socrates is mortal4' ,in this case1 what we really know beyond reasonable doubt is that certain men1 ,a1 ,b1 ,c1 were mortal1 since1 in fact1 they have died4 ,if ,socrates is one of these men1 it is foolish to go the roundabout way through 'all men are mortal' to arrive at the conclusion that probably ,socrates is mortal4 ,if ,socrates is not one of the men on whom our induction is based1 we shall still do better to argue straight from our ,a1 ,b1 ,c1 to ,socrates1 than to go round by the general proposition1 'all men are mortal'4 ,for the probability that ,socrates is mortal is greater1 on our data1 than the probability that all men are mortal4 7,this is obvious1 because if all men are mortal1 so is ,socrates2 but if ,socrates is mortal1 it does not follow that all men are mortal47 ,hence we shall reach the conclusion that ,socrates is mortal with a greater approach to certainty if we make our argument purely inductive than if we go by way of 'all men are mortal' and then use deduction4 ,this illustrates the difference between general propositions known a priori such as 'two and two are four'1 and empirical generalizations such as 'all men are mortal'4 ,in regard to the former1 deduction is the right mode of argument1 whereas in regard to the latter1 induction is always theoretically preferable1 and warrants a greater confidence in the truth of our conclusion1 because all empirical generalizations are more uncertain than the instances of them4 ,we have now seen that there are propositions known a priori1 and that among them are the propositions of logic and pure mathematics1 as well as the fundamental propositions of ethics4 ,the question which must next occupy us is this3 ,how is it possible that there should be such knowledge8 ,and more particularly1 how can there be knowledge of general propositions in cases where we have not examined all the instances1 and indeed never can examine them all1 because their number is infinite8 ,these questions1 which were first brought prominently forward by the ,german philosopher ,kant 7#agbd-ahjd71 are very difficult1 and historically very important4 ,,chapter ,,viii4 ,,how ,a ,,priori ,,knowledge ,,is ,,possible ,immanuel ,kant is generally regarded as the greatest of the modern philosophers4 ,though he lived through the ,seven ,years ,war and the ,french ,revolution1 he never interrupted his teaching of philosophy at ,knigsberg in ,east ,prussia4 ,his most distinctive contribution was the invention of what he called the 'critical' philosophy1 which1 assuming as a datum that there is knowledge of various kinds1 inquired how such knowledge comes to be possible1 and deduced1 from the answer to this inquiry1 many metaphysical results as to the nature of the world4 ,whether these results were valid may well be doubted4 ,but ,kant undoubtedly deserves credit for two things3 first1 for having perceived that we have a priori knowledge which is not purely 'analytic'1 i4e4 such that the opposite would be self-contradictory1 and secondly1 for having made evident the philosophical importance of the theory of knowledge4 ,before the time of ,kant1 it was generally held that whatever knowledge was a priori must be 'analytic'4 ,what this word means will be best illustrated by examples4 ,if ,i say1 ',a bald man is a man'1 ',a plane figure is a figure'1 ',a bad poet is a poet'1 ,i make a purely analytic judgement3 the subject spoken about is given as having at least two properties1 of which one is singled out to be asserted of it4 ,such propositions as the above are trivial1 and would never be enunciated in real life except by an orator preparing the way for a piece of sophistry4 ,they are called 'analytic' because the predicate is obtained by merely analysing the subject4 ,before the time of ,kant it was thought that all judgements of which we could be certain a priori were of this kind3 that in all of them there was a predicate which was only part of the subject of which it was asserted4 ,if this were so1 we should be involved in a definite contradiction if we attempted to deny anything that could be known a priori4 ',a bald man is not bald' would assert and deny baldness of the same man1 and would therefore contradict itself4 ,thus according to the philosophers before ,kant1 the law of contradiction1 which asserts that nothing can at the same time have and not have a certain property1 sufficed to establish the truth of all a priori knowledge4 ,hume 7#agaa-gf71 who preceded ,kant1 accepting the usual view as to what makes knowledge a priori1 discovered that1 in many cases which had previously been supposed analytic1 and notably in the case of cause and effect1 the connexion was really synthetic4 ,before ,hume1 rationalists at least had supposed that the effect could be logically deduced from the cause1 if only we had sufficient knowledge4 ,hume argued--correctly1 as would now be generally admitted--that this could not be done4 ,hence he inferred the far more doubtful proposition that nothing could be known a priori about the connexion of cause and effect4 ,kant1 who had been educated in the rationalist tradition1 was much perturbed by ,hume's scepticism1 and endeavoured to find an answer to it4 ,he perceived that not only the connexion of cause and effect1 but all the propositions of arithmetic and geometry1 are 'synthetic'1 i4e4 not analytic3 in all these propositions1 no analysis of the subject will reveal the predicate4 ,his stock instance was the proposition #g #e #ab4 ,he pointed out1 quite truly1 that #g and #e have to be put together to give #ab3 the idea of #ab is not contained in them1 nor even in the idea of adding them together4 ,thus he was led to the conclusion that all pure mathematics1 though a priori1 is synthetic2 and this conclusion raised a new problem of which he endeavoured to find the solution4 ,the question which ,kant put at the beginning of his philosophy1 namely ',how is pure mathematics possible8' is an interesting and difficult one1 to which every philosophy which is not purely sceptical must find some answer4 ,the answer of the pure empiricists1 that our mathematical knowledge is derived by induction from particular instances1 we have already seen to be inadequate1 for two reasons3 first1 that the validity of the inductive principle itself cannot be proved by induction2 secondly1 that the general propositions of mathematics1 such as 'two and two always make four'1 can obviously be known with certainty by consideration of a single instance1 and gain nothing by enumeration of other cases in which they have been found to be true4 ,thus our knowledge of the general propositions of mathematics 7and the same applies to logic7 must be accounted for otherwise than our 7merely probable7 knowledge of empirical generalizations such as 'all men are mortal'4 ,the problem arises through the fact that such knowledge is general1 whereas all experience is particular4 ,it seems strange that we should apparently be able to know some truths in advance about particular things of which we have as yet no experience2 but it cannot easily be doubted that logic and arithmetic will apply to such things4 ,we do not know who will be the inhabitants of ,london a hundred years hence2 but we know that any two of them and any other two of them will make four of them4 ,this apparent power of anticipating facts about things of which we have no experience is certainly surprising4 ,kant's solution of the problem1 though not valid in my opinion1 is interesting4 ,it is1 however1 very difficult1 and is differently understood by different philosophers4 ,we can1 therefore1 only give the merest outline of it1 and even that will be thought misleading by many exponents of ,kant's system4 ,what ,kant maintained was that in all our experience there are two elements to be distinguished1 the one due to the object 7i4e4 to what we have called the 'physical object'71 the other due to our own nature4 ,we saw1 in discussing matter and sense-data1 that the physical object is different from the associated sense-data1 and that the sense-data are to be regarded as resulting from an interaction between the physical object and ourselves4 ,so far1 we are in agreement with ,kant4 ,but what is distinctive of ,kant is the way in which he apportions the shares of ourselves and the physical object respectively4 ,he considers that the crude material given in sensation--the colour1 hardness1 etc4--is due to the object1 and that what we supply is the arrangement in space and time1 and all the relations between sense-data which result from comparison or from considering one as the cause of the other or in any other way4 ,his chief reason in favour of this view is that we seem to have a priori knowledge as to space and time and causality and comparison1 but not as to the actual crude material of sensation4 ,we can be sure1 he says1 that anything we shall ever experience must show the characteristics affirmed of it in our a priori knowledge1 because these characteristics are due to our own nature1 and therefore nothing can ever come into our experience without acquiring these characteristics4 ,the physical object1 which he calls the 'thing in itself'17#a7 he regards as essentially unknowable2 what can be known is the object as we have it in experience1 which he calls the 'phenomenon'4 ,the phenomenon1 being a joint product of us and the thing in itself1 is sure to have those characteristics which are due to us1 and is therefore sure to conform to our a priori knowledge4 ,hence this knowledge1 though true of all actual and possible experience1 must not be supposed to apply outside experience4 ,thus in spite of the existence of a priori knowledge1 we cannot know anything about the thing in itself or about what is not an actual or possible object of experience4 ,in this way he tries to reconcile and harmonize the contentions of the rationalists with the arguments of the empiricists4 7#a7 ,kant's 'thing in itself' is identical in definition with the physical object1 namely1 it is the cause of sensations4 ,in the properties deduced from the definition it is not identical1 since ,kant held 7in spite of some inconsistency as regards cause7 that we can know that none of the categories are applicable to the 'thing in itself'4 ,apart from minor grounds on which ,kant's philosophy may be criticized1 there is one main objection which seems fatal to any attempt to deal with the problem of a priori knowledge by his method4 ,the thing to be accounted for is our certainty that the facts must always conform to logic and arithmetic4 ,to say that logic and arithmetic are contributed by us does not account for this4 ,our nature is as much a fact of the existing world as anything1 and there can be no certainty that it will remain constant4 ,it might happen1 if ,kant is right1 that to-morrow our nature would so change as to make two and two become five4 ,this possibility seems never to have occurred to him1 yet it is one which utterly destroys the certainty and universality which he is anxious to vindicate for arithmetical propositions4 ,it is true that this possibility1 formally1 is inconsistent with the ,kantian view that time itself is a form imposed by the subject upon phenomena1 so that our real ,self is not in time and has no to-morrow4 ,but he will still have to suppose that the time-order of phenomena is determined by characteristics of what is behind phenomena1 and this suffices for the substance of our argument4 ,reflection1 moreover1 seems to make it clear that1 if there is any truth in our arithmetical beliefs1 they must apply to things equally whether we think of them or not4 ,two physical objects and two other physical objects must make four physical objects1 even if physical objects cannot be experienced4 ,to assert this is certainly within the scope of what we mean when we state that two and two are four4 ,its truth is just as indubitable as the truth of the assertion that two phenomena and two other phenomena make four phenomena4 ,thus ,kant's solution unduly limits the scope of a priori propositions1 in addition to failing in the attempt at explaining their certainty4 ,apart from the special doctrines advocated by ,kant1 it is very common among philosophers to regard what is a priori as in some sense mental1 as concerned rather with the way we must think than with any fact of the outer world4 ,we noted in the preceding chapter the three principles commonly called 'laws of thought'4 ,the view which led to their being so named is a natural one1 but there are strong reasons for thinking that it is erroneous4 ,let us take as an illustration the law of contradiction4 ,this is commonly stated in the form ',nothing can both be and not be'1 which is intended to express the fact that nothing can at once have and not have a given quality4 ,thus1 for example1 if a tree is a beech it cannot also be not a beech2 if my table is rectangular it cannot also be not rectangular1 and so on4 ,now what makes it natural to call this principle a law of thought is that it is by thought rather than by outward observation that we persuade ourselves of its necessary truth4 ,when we have seen that a tree is a beech1 we do not need to look again in order to ascertain whether it is also not a beech2 thought alone makes us know that this is impossible4 ,but the conclusion that the law of contradiction is a law of thought is nevertheless erroneous4 ,what we believe1 when we believe the law of contradiction1 is not that the mind is so made that it must believe the law of contradiction4 ,this belief is a subsequent result of psychological reflection1 which presupposes the belief in the law of contradiction4 ,the belief in the law of contradiction is a belief about things1 not only about thoughts4 ,it is not1 e4g41 the belief that if we think a certain tree is a beech1 we cannot at the same time think that it is not a beech2 it is the belief that if the tree is a beech1 it cannot at the same time be not a beech4 ,thus the law of contradiction is about things1 and not merely about thoughts2 and although belief in the law of contradiction is a thought1 the law of contradiction itself is not a thought1 but a fact concerning the things in the world4 ,if this1 which we believe when we believe the law of contradiction1 were not true of the things in the world1 the fact that we were compelled to think it true would not save the law of contradiction from being false2 and this shows that the law is not a law of thought4 ,a similar argument applies to any other a priori judgement4 ,when we judge that two and two are four1 we are not making a judgement about our thoughts1 but about all actual or possible couples4 ,the fact that our minds are so constituted as to believe that two and two are four1 though it is true1 is emphatically not what we assert when we assert that two and two are four4 ,and no fact about the constitution of our minds could make it true that two and two are four4 ,thus our a priori knowledge1 if it is not erroneous1 is not merely knowledge about the constitution of our minds1 but is applicable to whatever the world may contain1 both what is mental and what is non-mental4 ,the fact seems to be that all our a priori knowledge is concerned with entities which do not1 properly speaking1 exist1 either in the mental or in the physical world4 ,these entities are such as can be named by parts of speech which are not substantives2 they are such entities as qualities and relations4 ,suppose1 for instance1 that ,i am in my room4 ,i exist1 and my room exists2 but does 'in' exist8 ,yet obviously the word 'in' has a meaning2 it denotes a relation which holds between me and my room4 ,this relation is something1 although we cannot say that it exists in the same sense in which ,i and my room exist4 ,the relation 'in' is something which we can think about and understand1 for1 if we could not understand it1 we could not understand the sentence ',i am in my room'4 ,many philosophers1 following ,kant1 have maintained that relations are the work of the mind1 that things in themselves have no relations1 but that the mind brings them together in one act of thought and thus produces the relations which it judges them to have4 ,this view1 however1 seems open to objections similar to those which we urged before against ,kant4 ,it seems plain that it is not thought which produces the truth of the proposition ',i am in my room'4 ,it may be true that an earwig is in my room1 even if neither ,i nor the earwig nor any one else is aware of this truth2 for this truth concerns only the earwig and the room1 and does not depend upon anything else4 ,thus relations1 as we shall see more fully in the next chapter1 must be placed in a world which is neither mental nor physical4 ,this world is of great importance to philosophy1 and in particular to the problems of a priori knowledge4 ,in the next chapter we shall proceed to develop its nature and its bearing upon the questions with which we have been dealing4 ,,chapter ,,ix4 ,,the ,,world ,,of ,,universals ,at the end of the preceding chapter we saw that such entities as relations appear to have a being which is in some way different from that of physical objects1 and also different from that of minds and from that of sense-data4 ,in the present chapter we have to consider what is the nature of this kind of being1 and also what objects there are that have this kind of being4 ,we will begin with the latter question4 ,the problem with which we are now concerned is a very old one1 since it was brought into philosophy by ,plato4 ,plato's 'theory of ideas' is an attempt to solve this very problem1 and in my opinion it is one of the most successful attempts hitherto made4 ,the theory to be advocated in what follows is largely ,plato's1 with merely such modifications as time has shown to be necessary4 ,the way the problem arose for ,plato was more or less as follows4 ,let us consider1 say1 such a notion as justice4 ,if we ask ourselves what justice is1 it is natural to proceed by considering this1 that1 and the other just act1 with a view to discovering what they have in common4 ,they must all1 in some sense1 partake of a common nature1 which will be found in whatever is just and in nothing else4 ,this common nature1 in virtue of which they are all just1 will be justice itself1 the pure essence the admixture of which with facts of ordinary life produces the multiplicity of just acts4 ,similarly with any other word which may be applicable to common facts1 such as 'whiteness' for example4 ,the word will be applicable to a number of particular things because they all participate in a common nature or essence4 ,this pure essence is what ,plato calls an 'idea' or 'form'4 7,it must not be supposed that 'ideas'1 in his sense1 exist in minds1 though they may be apprehended by minds47 ,the 'idea' justice is not identical with anything that is just3 it is something other than particular things1 which particular things partake of4 ,not being particular1 it cannot itself exist in the world of sense4 ,moreover it is not fleeting or changeable like the things of sense3 it is eternally itself1 immutable and indestructible4 ,thus ,plato is led to a supra-sensible world1 more real than the common world of sense1 the unchangeable world of ideas1 which alone gives to the world of sense whatever pale reflection of reality may belong to it4 ,the truly real world1 for ,plato1 is the world of ideas2 for whatever we may attempt to say about things in the world of sense1 we can only succeed in saying that they participate in such and such ideas1 which1 therefore1 constitute all their character4 ,hence it is easy to pass on into a mysticism4 ,we may hope1 in a mystic illumination1 to see the ideas as we see objects of sense2 and we may imagine that the ideas exist in heaven4 ,these mystical developments are very natural1 but the basis of the theory is in logic1 and it is as based in logic that we have to consider it4 ,the word 'idea' has acquired1 in the course of time1 many associations which are quite misleading when applied to ,plato's 'ideas'4 ,we shall therefore use the word 'universal' instead of the word 'idea'1 to describe what ,plato meant4 ,the essence of the sort of entity that ,plato meant is that it is opposed to the particular things that are given in sensation4 ,we speak of whatever is given in sensation1 or is of the same nature as things given in sensation1 as a particular2 by opposition to this1 a universal will be anything which may be shared by many particulars1 and has those characteristics which1 as we saw1 distinguish justice and whiteness from just acts and white things4 ,when we examine common words1 we find that1 broadly speaking1 proper names stand for particulars1 while other substantives1 adjectives1 prepositions1 and verbs stand for universals4 ,pronouns stand for particulars1 but are ambiguous3 it is only by the context or the circumstances that we know what particulars they stand for4 ,the word 'now' stands for a particular1 namely the present moment2 but like pronouns1 it stands for an ambiguous particular1 because the present is always changing4 ,it will be seen that no sentence can be made up without at least one word which denotes a universal4 ,the nearest approach would be some such statement as ',i like this'4 ,but even here the word 'like' denotes a universal1 for ,i may like other things1 and other people may like things4 ,thus all truths involve universals1 and all knowledge of truths involves acquaintance with universals4 ,seeing that nearly all the words to be found in the dictionary stand for universals1 it is strange that hardly anybody except students of philosophy ever realizes that there are such entities as universals4 ,we do not naturally dwell upon those words in a sentence which do not stand for particulars2 and if we are forced to dwell upon a word which stands for a universal1 we naturally think of it as standing for some one of the particulars that come under the universal4 ,when1 for example1 we hear the sentence1 ',charles ,i's head was cut off'1 we may naturally enough think of ,charles ,i1 of ,charles ,i's head1 and of the operation of cutting off his head1 which are all particulars2 but we do not naturally dwell upon what is meant by the word 'head' or the word 'cut'1 which is a universal3 ,we feel such words to be incomplete and insubstantial2 they seem to demand a context before anything can be done with them4 ,hence we succeed in avoiding all notice of universals as such1 until the study of philosophy forces them upon our attention4 ,even among philosophers1 we may say1 broadly1 that only those universals which are named by adjectives or substantives have been much or often recognized1 while those named by verbs and prepositions have been usually overlooked4 ,this omission has had a very great effect upon philosophy2 it is hardly too much to say that most metaphysics1 since ,spinoza1 has been largely determined by it4 ,the way this has occurred is1 in outline1 as follows3 ,speaking generally1 adjectives and common nouns express qualities or properties of single things1 whereas prepositions and verbs tend to express relations between two or more things4 ,thus the neglect of prepositions and verbs led to the belief that every proposition can be regarded as attributing a property to a single thing1 rather than as expressing a relation between two or more things4 ,hence it was supposed that1 ultimately1 there can be no such entities as relations between things4 ,hence either there can be only one thing in the universe1 or1 if there are many things1 they cannot possibly interact in any way1 since any interaction would be a relation1 and relations are impossible4 ,the first of these views1 advocated by ,spinoza and held in our own day by ,bradley and many other philosophers1 is called monism2 the second1 advocated by ,leibniz but not very common nowadays1 is called monadism1 because each of the isolated things is called a monad4 ,both these opposing philosophies1 interesting as they are1 result1 in my opinion1 from an undue attention to one sort of universals1 namely the sort represented by adjectives and substantives rather than by verbs and prepositions4 ,as a matter of fact1 if any one were anxious to deny altogether that there are such things as universals1 we should find that we cannot strictly prove that there are such entities as qualities1 i4e4 the universals represented by adjectives and substantives1 whereas we can prove that there must be relations1 i4e4 the sort of universals generally represented by verbs and prepositions4 ,let us take in illustration the universal whiteness4 ,if we believe that there is such a universal1 we shall say that things are white because they have the quality of whiteness4 ,this view1 however1 was strenuously denied by ,berkeley and ,hume1 who have been followed in this by later empiricists4 ,the form which their denial took was to deny that there are such things as 'abstract ideas '4 ,when we want to think of whiteness1 they said1 we form an image of some particular white thing1 and reason concerning this particular1 taking care not to deduce anything concerning it which we cannot see to be equally true of any other white thing4 ,as an account of our actual mental processes1 this is no doubt largely true4 ,in geometry1 for example1 when we wish to prove something about all triangles1 we draw a particular triangle and reason about it1 taking care not to use any characteristic which it does not share with other triangles4 ,the beginner1 in order to avoid error1 often finds it useful to draw several triangles1 as unlike each other as possible1 in order to make sure that his reasoning is equally applicable to all of them4 ,but a difficulty emerges as soon as we ask ourselves how we know that a thing is white or a triangle4 ,if we wish to avoid the universals whiteness and triangularity1 we shall choose some particular patch of white or some particular triangle1 and say that anything is white or a triangle if it has the right sort of resemblance to our chosen particular4 ,but then the resemblance required will have to be a universal4 ,since there are many white things1 the resemblance must hold between many pairs of particular white things2 and this is the characteristic of a universal4 ,it will be useless to say that there is a different resemblance for each pair1 for then we shall have to say that these resemblances resemble each other1 and thus at last we shall be forced to admit resemblance as a universal4 ,the relation of resemblance1 therefore1 must be a true universal4 ,and having been forced to admit this universal1 we find that it is no longer worth while to invent difficult and unplausible theories to avoid the admission of such universals as whiteness and triangularity4 ,berkeley and ,hume failed to perceive this refutation of their rejection of 'abstract ideas'1 because1 like their adversaries1 they only thought of qualities1 and altogether ignored relations as universals4 ,we have therefore here another respect in which the rationalists appear to have been in the right as against the empiricists1 although1 owing to the neglect or denial of relations1 the deductions made by rationalists were1 if anything1 more apt to be mistaken than those made by empiricists4 ,having now seen that there must be such entities as universals1 the next point to be proved is that their being is not merely mental4 ,by this is meant that whatever being belongs to them is independent of their being thought of or in any way apprehended by minds4 ,we have already touched on this subject at the end of the preceding chapter1 but we must now consider more fully what sort of being it is that belongs to universals4 ,consider such a proposition as ',edinburgh is north of ,london'4 ,here we have a relation between two places1 and it seems plain that the relation subsists independently of our knowledge of it4 ,when we come to know that ,edinburgh is north of ,london1 we come to know something which has to do only with ,edinburgh and ,london3 we do not cause the truth of the proposition by coming to know it1 on the contrary we merely apprehend a fact which was there before we knew it4 ,the part of the earth's surface where ,edinburgh stands would be north of the part where ,london stands1 even if there were no human being to know about north and south1 and even if there were no minds at all in the universe4 ,this is1 of course1 denied by many philosophers1 either for ,berkeley's reasons or for ,kant's4 ,but we have already considered these reasons1 and decided that they are inadequate4 ,we may therefore now assume it to be true that nothing mental is presupposed in the fact that ,edinburgh is north of ,london4 ,but this fact involves the relation 'north of'1 which is a universal2 and it would be impossible for the whole fact to involve nothing mental if the relation 'north of'1 which is a constituent part of the fact1 did involve anything mental4 ,hence we must admit that the relation1 like the terms it relates1 is not dependent upon thought1 but belongs to the independent world which thought apprehends but does not create4 ,this conclusion1 however1 is met by the difficulty that the relation 'north of' does not seem to exist in the same sense in which ,edinburgh and ,london exist4 ,if we ask ',where and when does this relation exist8' the answer must be ',nowhere and nowhen'4 ,there is no place or time where we can find the relation 'north of'4 ,it does not exist in ,edinburgh any more than in ,london1 for it relates the two and is neutral as between them4 ,nor can we say that it exists at any particular time4 ,now everything that can be apprehended by the senses or by introspection exists at some particular time4 ,hence the relation 'north of' is radically different from such things4 ,it is neither in space nor in time1 neither material nor mental2 yet it is something4 ,it is largely the very peculiar kind of being that belongs to universals which has led many people to suppose that they are really mental4 ,we can think of a universal1 and our thinking then exists in a perfectly ordinary sense1 like any other mental act4 ,suppose1 for example1 that we are thinking of whiteness4 ,then in one sense it may be said that whiteness is 'in our mind'4 ,we have here the same ambiguity as we noted in discussing ,berkeley in ,chapter ,,iv4 ,in the strict sense1 it is not whiteness that is in our mind1 but the act of thinking of whiteness4 ,the connected ambiguity in the word 'idea'1 which we noted at the same time1 also causes confusion here4 ,in one sense of this word1 namely the sense in which it denotes the object of an act of thought1 whiteness is an 'idea'4 ,hence1 if the ambiguity is not guarded against1 we may come to think that whiteness is an 'idea' in the other sense1 i4e4 an act of thought2 and thus we come to think that whiteness is mental4 ,but in so thinking1 we rob it of its essential quality of universality4 ,one man's act of thought is necessarily a different thing from another man's2 one man's act of thought at one time is necessarily a different thing from the same man's act of thought at another time4 ,hence1 if whiteness were the thought as opposed to its object1 no two different men could think of it1 and no one man could think of it twice4 ,that which many different thoughts of whiteness have in common is their object1 and this object is different from all of them4 ,thus universals are not thoughts1 though when known they are the objects of thoughts4 ,we shall find it convenient only to speak of things existing when they are in time1 that is to say1 when we can point to some time at which they exist 7not excluding the possibility of their existing at all times74 ,thus thoughts and feelings1 minds and physical objects exist4 ,but universals do not exist in this sense2 we shall say that they subsist or have being1 where 'being' is opposed to 'existence' as being timeless4 ,the world of universals1 therefore1 may also be described as the world of being4 ,the world of being is unchangeable1 rigid1 exact1 delightful to the mathematician1 the logician1 the builder of metaphysical systems1 and all who love perfection more than life4 ,the world of existence is fleeting1 vague1 without sharp boundaries1 without any clear plan or arrangement1 but it contains all thoughts and feelings1 all the data of sense1 and all physical objects1 everything that can do either good or harm1 everything that makes any difference to the value of life and the world4 ,according to our temperaments1 we shall prefer the contemplation of the one or of the other4 ,the one we do not prefer will probably seem to us a pale shadow of the one we prefer1 and hardly worthy to be regarded as in any sense real4 ,but the truth is that both have the same claim on our impartial attention1 both are real1 and both are important to the metaphysician4 ,indeed no sooner have we distinguished the two worlds than it becomes necessary to consider their relations4 ,but first of all we must examine our knowledge of universals4 ,this consideration will occupy us in the following chapter1 where we shall find that it solves the problem of a priori knowledge1 from which we were first led to consider universals4 ,,chapter ,x4 ,,on ,,our ,,knowledge ,,of ,,universals ,in regard to one man's knowledge at a given time1 universals1 like particulars1 may be divided into those known by acquaintance1 those known only by description1 and those not known either by acquaintance or by description4 ,let us consider first the knowledge of universals by acquaintance4 ,it is obvious1 to begin with1 that we are acquainted with such universals as white1 red1 black1 sweet1 sour1 loud1 hard1 etc41 i4e4 with qualities which are exemplified in sense-data4 ,when we see a white patch1 we are acquainted1 in the first instance1 with the particular patch2 but by seeing many white patches1 we easily learn to abstract the whiteness which they all have in common1 and in learning to do this we are learning to be acquainted with whiteness4 ,a similar process will make us acquainted with any other universal of the same sort4 ,universals of this sort may be called 'sensible qualities'4 ,they can be apprehended with less effort of abstraction than any others1 and they seem less removed from particulars than other universals are4 ,we come next to relations4 ,the easiest relations to apprehend are those which hold between the different parts of a single complex sense-datum4 ,for example1 ,i can see at a glance the whole of the page on which ,i am writing2 thus the whole page is included in one sense-datum4 ,but ,i perceive that some parts of the page are to the left of other parts1 and some parts are above other parts4 ,the process of abstraction in this case seems to proceed somewhat as follows3 ,i see successively a number of sense-data in which one part is to the left of another2 ,i perceive1 as in the case of different white patches1 that all these sense-data have something in common1 and by abstraction ,i find that what they have in common is a certain relation between their parts1 namely the relation which ,i call 'being to the left of'4 ,in this way ,i become acquainted with the universal relation4 ,in like manner ,i become aware of the relation of before and after in time4 ,suppose ,i hear a chime of bells3 when the last bell of the chime sounds1 ,i can retain the whole chime before my mind1 and ,i can perceive that the earlier bells came before the later ones4 ,also in memory ,i perceive that what ,i am remembering came before the present time4 ,from either of these sources ,i can abstract the universal relation of before and after1 just as ,i abstracted the universal relation 'being to the left of'4 ,thus time-relations1 like space-relations1 are among those with which we are acquainted4 ,another relation with which we become acquainted in much the same way is resemblance4 ,if ,i see simultaneously two shades of green1 ,i can see that they resemble each other2 if ,i also see a shade of red3 at the same time1 ,i can see that the two greens have more resemblance to each other than either has to the red4 ,in this way ,i become acquainted with the universal resemblance or similarity4 ,between universals1 as between particulars1 there are relations of which we may be immediately aware4 ,we have just seen that we can perceive that the resemblance between two shades of green is greater than the resemblance between a shade of red and a shade of green4 ,here we are dealing with a relation1 namely 'greater than'1 between two relations4 ,our knowledge of such relations1 though it requires more power of abstraction than is required for perceiving the qualities of sense-data1 appears to be equally immediate1 and 7at least in some cases7 equally indubitable4 ,thus there is immediate knowledge concerning universals as well as concerning sense-data4 ,returning now to the problem of a priori knowledge1 which we left unsolved when we began the consideration of universals1 we find ourselves in a position to deal with it in a much more satisfactory manner than was possible before4 ,let us revert to the proposition 'two and two are four'4 ,it is fairly obvious1 in view of what has been said1 that this proposition states a relation between the universal 'two' and the universal 'four'4 ,this suggests a proposition which we shall now endeavour to establish3 namely1 ,all a priori knowledge deals exclusively with the relations of universals4 ,this proposition is of great importance1 and goes a long way towards solving our previous difficulties concerning a priori knowledge4 ,the only case in which it might seem1 at first sight1 as if our proposition were untrue1 is the case in which an a priori proposition states that all of one class of particulars belong to some other class1 or 7what comes to the same thing7 that all particulars having some one property also have some other4 ,in this case it might seem as though we were dealing with the particulars that have the property rather than with the property4 ,the proposition 'two and two are four' is really a case in point1 for this may be stated in the form 'any two and any other two are four'1 or 'any collection formed of two twos is a collection of four'4 ,if we can show that such statements as this really deal only with universals1 our proposition may be regarded as proved4 ,one way of discovering what a proposition deals with is to ask ourselves what words we must understand--in other words1 what objects we must be acquainted with--in order to see what the proposition means4 ,as soon as we see what the proposition means1 even if we do not yet know whether it is true or false1 it is evident that we must have acquaintance with whatever is really dealt with by the proposition4 ,by applying this test1 it appears that many propositions which might seem to be concerned with particulars are really concerned only with universals4 ,in the special case of 'two and two are four'1 even when we interpret it as meaning 'any collection formed of two twos is a collection of four'1 it is plain that we can understand the proposition1 i4e4 we can see what it is that it asserts1 as soon as we know what is meant by 'collection' and 'two' and 'four'4 ,it is quite unnecessary to know all the couples in the world3 if it were necessary1 obviously we could never understand the proposition1 since the couples are infinitely numerous and therefore cannot all be known to us4 ,thus although our general statement implies statements about particular couples1 as soon as we know that there are such particular couples1 yet it does not itself assert or imply that there are such particular couples1 and thus fails to make any statement whatever about any actual particular couple4 ,the statement made is about 'couple'1 the universal1 and not about this or that couple4 ,thus the statement 'two and two are four' deals exclusively with universals1 and therefore may be known by anybody who is acquainted with the universals concerned and can perceive the relation between them which the statement asserts4 ,it must be taken as a fact1 discovered by reflecting upon our knowledge1 that we have the power of sometimes perceiving such relations between universals1 and therefore of sometimes knowing general a priori propositions such as those of arithmetic and logic4 ,the thing that seemed mysterious1 when we formerly considered such knowledge1 was that it seemed to anticipate and control experience4 ,this1 however1 we can now see to have been an error4 ,no fact concerning anything capable of being experienced can be known independently of experience4 ,we know a priori that two things and two other things together make four things1 but we do not know a priori that if ,brown and ,jones are two1 and ,robinson and ,smith are two1 then ,brown and ,jones and ,robinson and ,smith are four4 ,the reason is that this proposition cannot be understood at all unless we know that there are such people as ,brown and ,jones and ,robinson and ,smith1 and this we can only know by experience4 ,hence1 although our general proposition is a priori1 all its applications to actual particulars involve experience and therefore contain an empirical element4 ,in this way what seemed mysterious in our a priori knowledge is seen to have been based upon an error4 ,it will serve to make the point clearer if we contrast our genuine a priori judgement with an empirical generalization1 such as 'all men are mortals'4 ,here as before1 we can understand what the proposition means as soon as we understand the universals involved1 namely man and mortal4 ,it is obviously unnecessary to have an individual acquaintance with the whole human race in order to understand what our proposition means4 ,thus the difference between an a priori general proposition and an empirical generalization does not come in the meaning of the proposition2 it comes in the nature of the evidence for it4 ,in the empirical case1 the evidence consists in the particular instances4 ,we believe that all men are mortal because we know that there are innumerable instances of men dying1 and no instances of their living beyond a certain age4 ,we do not believe it because we see a connexion between the universal man and the universal mortal4 ,it is true that if physiology can prove1 assuming the general laws that govern living bodies1 that no living organism can last for ever1 that gives a connexion between man and mortality which would enable us to assert our proposition without appealing to the special evidence of men dying4 ,but that only means that our generalization has been subsumed under a wider generalization1 for which the evidence is still of the same kind1 though more extensive4 ,the progress of science is constantly producing such subsumptions1 and therefore giving a constantly wider inductive basis for scientific generalizations4 ,but although this gives a greater degree of certainty1 it does not give a different kind3 the ultimate ground remains inductive1 i4e4 derived from instances1 and not an a priori connexion of universals such as we have in logic and arithmetic4 ,two opposite points are to be observed concerning a priori general propositions4 ,the first is that1 if many particular instances are known1 our general proposition may be arrived at in the first instance by induction1 and the connexion of universals may be only subsequently perceived4 ,for example1 it is known that if we draw perpendiculars to the sides of a triangle from the opposite angles1 all three perpendiculars meet in a point4 ,it would be quite possible to be first led to this proposition by actually drawing perpendiculars in many cases1 and finding that they always met in a point2 this experience might lead us to look for the general proof and find it4 ,such cases are common in the experience of every mathematician4 ,the other point is more interesting1 and of more philosophical importance4 ,it is1 that we may sometimes know a general proposition in cases where we do not know a single instance of it4 ,take such a case as the following3 ,we know that any two numbers can be multiplied together1 and will give a third called their product4 ,we know that all pairs of integers the product of which is less than #ajj have been actually multiplied together1 and the value of the product recorded in the multiplication table4 ,but we also know that the number of integers is infinite1 and that only a finite number of pairs of integers ever have been or ever will be thought of by human beings4 ,hence it follows that there are pairs of integers which never have been and never will be thought of by human beings1 and that all of them deal with integers the product of which is over #ajj4 ,hence we arrive at the proposition3 ',all products of two integers1 which never have been and never will be thought of by any human being1 are over #ajj4' ,here is a general proposition of which the truth is undeniable1 and yet1 from the very nature of the case1 we can never give an instance2 because any two numbers we may think of are excluded by the terms of the proposition4 ,this possibility1 of knowledge of general propositions of which no instance can be given1 is often denied1 because it is not perceived that the knowledge of such propositions only requires a knowledge of the relations of universals1 and does not require any knowledge of instances of the universals in question4 ,yet the knowledge of such general propositions is quite vital to a great deal of what is generally admitted to be known4 ,for example1 we saw1 in our early chapters1 that knowledge of physical objects1 as opposed to sense-data1 is only obtained by an inference1 and that they are not things with which we are acquainted4 ,hence we can never know any proposition of the form 'this is a physical object'1 where 'this' is something immediately known4 ,it follows that all our knowledge concerning physical objects is such that no actual instance can be given4 ,we can give instances of the associated sense-data1 but we cannot give instances of the actual physical objects4 ,hence our knowledge as to physical objects depends throughout upon this possibility of general knowledge where no instance can be given4 ,and the same applies to our knowledge of other people's minds1 or of any other class of things of which no instance is known to us by acquaintance4 ,we may now take a survey of the sources of our knowledge1 as they have appeared in the course of our analysis4 ,we have first to distinguish knowledge of things and knowledge of truths4 ,in each there are two kinds1 one immediate and one derivative4 ,our immediate knowledge of things1 which we called acquaintance1 consists of two sorts1 according as the things known are particulars or universals4 ,among particulars1 we have acquaintance with sense-data and 7probably7 with ourselves4 ,among universals1 there seems to be no principle by which we can decide which can be known by acquaintance1 but it is clear that among those that can be so known are sensible qualities1 relations of space and time1 similarity1 and certain abstract logical universals4 ,our derivative knowledge of things1 which we call knowledge by description1 always involves both acquaintance with something and knowledge of truths4 ,our immediate knowledge of truths may be called intuitive knowledge1 and the truths so known may be called self-evident truths4 ,among such truths are included those which merely state what is given in sense1 and also certain abstract logical and arithmetical principles1 and 7though with less certainty7 some ethical propositions4 ,our derivative knowledge of truths consists of everything that we can deduce from self-evident truths by the use of self-evident principles of deduction4 ,if the above account is correct1 all our knowledge of truths depends upon our intuitive knowledge4 ,it therefore becomes important to consider the nature and scope of intuitive knowledge1 in much the same way as1 at an earlier stage1 we considered the nature and scope of knowledge by acquaintance4 ,but knowledge of truths raises a further problem1 which does not arise in regard to knowledge of things1 namely the problem of error4 ,some of our beliefs turn out to be erroneous1 and therefore it becomes necessary to consider how1 if at all1 we can distinguish knowledge from error4 ,this problem does not arise with regard to knowledge by acquaintance1 for1 whatever may be the object of acquaintance1 even in dreams and hallucinations1 there is no error involved so long as we do not go beyond the immediate object3 error can only arise when we regard the immediate object1 i4e4 the sense-datum1 as the mark of some physical object4 ,thus the problems connected with knowledge of truths are more difficult than those connected with knowledge of things4 ,as the first of the problems connected with knowledge of truths1 let us examine the nature and scope of our intuitive judgements4 ,,chapter ,,xi4 ,,on ,,intuitive ,,knowledge ,there is a common impression that everything that we believe ought to be capable of proof1 or at least of being shown to be highly probable4 ,it is felt by many that a belief for which no reason can be given is an unreasonable belief4 ,in the main1 this view is just4 ,almost all our common beliefs are either inferred1 or capable of being inferred1 from other beliefs which may be regarded as giving the reason for them4 ,as a rule1 the reason has been forgotten1 or has even never been consciously present to our minds4 ,few of us ever ask ourselves1 for example1 what reason there is to suppose the food we are just going to eat will not turn out to be poison4 ,yet we feel1 when challenged1 that a perfectly good reason could be found1 even if we are not ready with it at the moment4 ,and in this belief we are usually justified4 ,but let us imagine some insistent ,socrates1 who1 whatever reason we give him1 continues to demand a reason for the reason4 ,we must sooner or later1 and probably before very long1 be driven to a point where we cannot find any further reason1 and where it becomes almost certain that no further reason is even theoretically discoverable4 ,starting with the common beliefs of daily life1 we can be driven back from point to point1 until we come to some general principle1 or some instance of a general principle1 which seems luminously evident1 and is not itself capable of being deduced from anything more evident4 ,in most questions of daily life1 such as whether our food is likely to be nourishing and not poisonous1 we shall be driven back to the inductive principle1 which we discussed in ,chapter ,,vi4 ,but beyond that1 there seems to be no further regress4 ,the principle itself is constantly used in our reasoning1 sometimes consciously1 sometimes unconsciously2 but there is no reasoning which1 starting from some simpler self-evident principle1 leads us to the principle of induction as its conclusion4 ,and the same holds for other logical principles4 ,their truth is evident to us1 and we employ them in constructing demonstrations2 but they themselves1 or at least some of them1 are incapable of demonstration4 ,self-evidence1 however1 is not confined to those among general principles which are incapable of proof4 ,when a certain number of logical principles have been admitted1 the rest can be deduced from them2 but the propositions deduced are often just as self-evident as those that were assumed without proof4 ,all arithmetic1 moreover1 can be deduced from the general principles of logic1 yet the simple propositions of arithmetic1 such as 'two and two are four'1 are just as self-evident as the principles of logic4 ,it would seem1 also1 though this is more disputable1 that there are some self-evident ethical principles1 such as 'we ought to pursue what is good'4 ,it should be observed that1 in all cases of general principles1 particular instances1 dealing with familiar things1 are more evident than the general principle4 ,for example1 the law of contradiction states that nothing can both have a certain property and not have it4 ,this is evident as soon as it is understood1 but it is not so evident as that a particular rose which we see cannot be both red and not red4 7,it is of course possible that parts of the rose may be red and parts not red1 or that the rose may be of a shade of pink which we hardly know whether to call red or not2 but in the former case it is plain that the rose as a whole is not red1 while in the latter case the answer is theoretically definite as soon as we have decided on a precise definition of 'red'47 ,it is usually through particular instances that we come to be able to see the general principle4 ,only those who are practised in dealing with abstractions can readily grasp a general principle without the help of instances4 ,in addition to general principles1 the other kind of self-evident truths are those immediately derived from sensation4 ,we will call such truths 'truths of perception'1 and the judgements expressing them we will call 'judgements of perception'4 ,but here a certain amount of care is required in getting at the precise nature of the truths that are self-evident4 ,the actual sense-data are neither true nor false4 ,a particular patch of colour which ,i see1 for example1 simply exists3 it is not the sort of thing that is true or false4 ,it is true that there is such a patch1 true that it has a certain shape and degree of brightness1 true that it is surrounded by certain other colours4 ,but the patch itself1 like everything else in the world of sense1 is of a radically different kind from the things that are true or false1 and therefore cannot properly be said to be true4 ,thus whatever self-evident truths may be obtained from our senses must be different from the sense-data from which they are obtained4 ,it would seem that there are two kinds of self-evident truths of perception1 though perhaps in the last analysis the two kinds may coalesce4 ,first1 there is the kind which simply asserts the existence of the sense-datum1 without in any way analysing it4 ,we see a patch of red1 and we judge 'there is such-and-such a patch of red'1 or more strictly 'there is that'2 this is one kind of intuitive judgement of perception4 ,the other kind arises when the object of sense is complex1 and we subject it to some degree of analysis4 ,if1 for instance1 we see a round patch of red1 we may judge 'that patch of red is round'4 ,this is again a judgement of perception1 but it differs from our previous kind4 ,in our present kind we have a single sense-datum which has both colour and shape3 the colour is red and the shape is round4 ,our judgement analyses the datum into colour and shape1 and then recombines them by stating that the red colour is round in shape4 ,another example of this kind of judgement is 'this is to the right of that'1 where 'this' and 'that' are seen simultaneously4 ,in this kind of judgement the sense-datum contains constituents which have some relation to each other1 and the judgement asserts that these constituents have this relation4 ,another class of intuitive judgements1 analogous to those of sense and yet quite distinct from them1 are judgements of memory4 ,there is some danger of confusion as to the nature of memory1 owing to the fact that memory of an object is apt to be accompanied by an image of the object1 and yet the image cannot be what constitutes memory4 ,this is easily seen by merely noticing that the image is in the present1 whereas what is remembered is known to be in the past4 ,moreover1 we are certainly able to some extent to compare our image with the object remembered1 so that we often know1 within somewhat wide limits1 how far our image is accurate2 but this would be impossible1 unless the object1 as opposed to the image1 were in some way before the mind4 ,thus the essence of memory is not constituted by the image1 but by having immediately before the mind an object which is recognized as past4 ,but for the fact of memory in this sense1 we should not know that there ever was a past at all1 nor should we be able to understand the word 'past'1 any more than a man born blind can understand the word 'light'4 ,thus there must be intuitive judgements of memory1 and it is upon them1 ultimately1 that all our knowledge of the past depends4 ,the case of memory1 however1 raises a difficulty1 for it is notoriously fallacious1 and thus throws doubt on the trustworthiness of intuitive judgements in general4 ,this difficulty is no light one4 ,but let us first narrow its scope as far as possible4 ,broadly speaking1 memory is trustworthy in proportion to the vividness of the experience and to its nearness in time4 ,if the house next door was struck by lightning half a minute ago1 my memory of what ,i saw and heard will be so reliable that it would be preposterous to doubt whether there had been a flash at all4 ,and the same applies to less vivid experiences1 so long as they are recent4 ,i am absolutely certain that half a minute ago ,i was sitting in the same chair in which ,i am sitting now4 ,going backward over the day1 ,i find things of which ,i am quite certain1 other things of which ,i am almost certain1 other things of which ,i can become certain by thought and by calling up attendant circumstances1 and some things of which ,i am by no means certain4 ,i am quite certain that ,i ate my breakfast this morning1 but if ,i were as indifferent to my breakfast as a philosopher should be1 ,i should be doubtful4 ,as to the conversation at breakfast1 ,i can recall some of it easily1 some with an effort1 some only with a large element of doubt1 and some not at all4 ,thus there is a continual gradation in the degree of self-evidence of what ,i remember1 and a corresponding gradation in the trustworthiness of my memory4 ,thus the first answer to the difficulty of fallacious memory is to say that memory has degrees of self-evidence1 and that these correspond to the degrees of its trustworthiness1 reaching a limit of perfect self-evidence and perfect trustworthiness in our memory of events which are recent and vivid4 ,it would seem1 however1 that there are cases of very firm belief in a memory which is wholly false4 ,it is probable that1 in these cases1 what is really remembered1 in the sense of being immediately before the mind1 is something other than what is falsely believed in1 though something generally associated with it4 ,george ,,iv is said to have at last believed that he was at the battle of ,waterloo1 because he had so often said that he was4 ,in this case1 what was immediately remembered was his repeated assertion2 the belief in what he was asserting 7if it existed7 would be produced by association with the remembered assertion1 and would therefore not be a genuine case of memory4 ,it would seem that cases of fallacious memory can probably all be dealt with in this way1 i4e4 they can be shown to be not cases of memory in the strict sense at all4 ,one important point about self-evidence is made clear by the case of memory1 and that is1 that self-evidence has degrees3 it is not a quality which is simply present or absent1 but a quality which may be more or less present1 in gradations ranging from absolute certainty down to an almost imperceptible faintness4 ,truths of perception and some of the principles of logic have the very highest degree of self-evidence2 truths of immediate memory have an almost equally high degree4 ,the inductive principle has less self-evidence than some of the other principles of logic1 such as 'what follows from a true premiss must be true'4 ,memories have a diminishing self-evidence as they become remoter and fainter2 the truths of logic and mathematics have 7broadly speaking7 less self-evidence as they become more complicated4 ,judgements of intrinsic ethical or aesthetic value are apt to have some self-evidence1 but not much4 ,degrees of self-evidence are important in the theory of knowledge1 since1 if propositions may 7as seems likely7 have some degree of self-evidence without being true1 it will not be necessary to abandon all connexion between self-evidence and truth1 but merely to say that1 where there is a conflict1 the more self-evident proposition is to be retained and the less self-evident rejected4 ,it seems1 however1 highly probable that two different notions are combined in 'self-evidence' as above explained2 that one of them1 which corresponds to the highest degree of self-evidence1 is really an infallible guarantee of truth1 while the other1 which corresponds to all the other degrees1 does not give an infallible guarantee1 but only a greater or less presumption4 ,this1 however1 is only a suggestion1 which we cannot as yet develop further4 ,after we have dealt with the nature of truth1 we shall return to the subject of self-evidence1 in connexion with the distinction between knowledge and error4 ,,chapter ,,xii4 ,,truth ,,and ,,falsehood ,our knowledge of truths1 unlike our knowledge of things1 has an opposite1 namely error4 ,so far as things are concerned1 we may know them or not know them1 but there is no positive state of mind which can be described as erroneous knowledge of things1 so long1 at any rate1 as we confine ourselves to knowledge by acquaintance4 ,whatever we are acquainted with must be something2 we may draw wrong inferences from our acquaintance1 but the acquaintance itself cannot be deceptive4 ,thus there is no dualism as regards acquaintance4 ,but as regards knowledge of truths1 there is a dualism4 ,we may believe what is false as well as what is true4 ,we know that on very many subjects different people hold different and incompatible opinions3 hence some beliefs must be erroneous4 ,since erroneous beliefs are often held just as strongly as true beliefs1 it becomes a difficult question how they are to be distinguished from true beliefs4 ,how are we to know1 in a given case1 that our belief is not erroneous8 ,this is a question of the very greatest difficulty1 to which no completely satisfactory answer is possible4 ,there is1 however1 a preliminary question which is rather less difficult1 and that is3 ,what do we mean by truth and falsehood8 ,it is this preliminary question which is to be considered in this chapter4 ,in this chapter we are not asking how we can know whether a belief is true or false3 we are asking what is meant by the question whether a belief is true or false4 ,it is to be hoped that a clear answer to this question may help us to obtain an answer to the question what beliefs are true1 but for the present we ask only ',what is truth8' and ',what is falsehood8' not ',what beliefs are true8' and ',what beliefs are false8' ,it is very important to keep these different questions entirely separate1 since any confusion between them is sure to produce an answer which is not really applicable to either4 ,there are three points to observe in the attempt to discover the nature of truth1 three requisites which any theory must fulfil4 7#a7 ,our theory of truth must be such as to admit of its opposite1 falsehood4 ,a good many philosophers have failed adequately to satisfy this condition3 they have constructed theories according to which all our thinking ought to have been true1 and have then had the greatest difficulty in finding a place for falsehood4 ,in this respect our theory of belief must differ from our theory of acquaintance1 since in the case of acquaintance it was not necessary to take account of any opposite4 7#b7 ,it seems fairly evident that if there were no beliefs there could be no falsehood1 and no truth either1 in the sense in which truth is correlative to falsehood4 ,if we imagine a world of mere matter1 there would be no room for falsehood in such a world1 and although it would contain what may be called 'facts'1 it would not contain any truths1 in the sense in which truths are things of the same kind as falsehoods4 ,in fact1 truth and falsehood are properties of beliefs and statements3 hence a world of mere matter1 since it would contain no beliefs or statements1 would also contain no truth or falsehood4 7#c7 ,but1 as against what we have just said1 it is to be observed that the truth or falsehood of a belief always depends upon something which lies outside the belief itself4 ,if ,i believe that ,charles ,i died on the scaffold1 ,i believe truly1 not because of any intrinsic quality of my belief1 which could be discovered by merely examining the belief1 but because of an historical event which happened two and a half centuries ago4 ,if ,i believe that ,charles ,i died in his bed1 ,i believe falsely3 no degree of vividness in my belief1 or of care in arriving at it1 prevents it from being false1 again because of what happened long ago1 and not because of any intrinsic property of my belief4 ,hence1 although truth and falsehood are properties of beliefs1 they are properties dependent upon the relations of the beliefs to other things1 not upon any internal quality of the beliefs4 ,the third of the above requisites leads us to adopt the view--which has on the whole been commonest among philosophers--that truth consists in some form of correspondence between belief and fact4 ,it is1 however1 by no means an easy matter to discover a form of correspondence to which there are no irrefutable objections4 ,by this partly--and partly by the feeling that1 if truth consists in a correspondence of thought with something outside thought1 thought can never know when truth has been attained--many philosophers have been led to try to find some definition of truth which shall not consist in relation to something wholly outside belief4 ,the most important attempt at a definition of this sort is the theory that truth consists in coherence4 ,it is said that the mark of falsehood is failure to cohere in the body of our beliefs1 and that it is the essence of a truth to form part of the completely rounded system which is ,the ,truth4 ,there is1 however1 a great difficulty in this view1 or rather two great difficulties4 ,the first is that there is no reason to suppose that only one coherent body of beliefs is possible4 ,it may be that1 with sufficient imagination1 a novelist might invent a past for the world that would perfectly fit on to what we know1 and yet be quite different from the real past4 ,in more scientific matters1 it is certain that there are often two or more hypotheses which account for all the known facts on some subject1 and although1 in such cases1 men of science endeavour to find facts which will rule out all the hypotheses except one1 there is no reason why they should always succeed4 ,in philosophy1 again1 it seems not uncommon for two rival hypotheses to be both able to account for all the facts4 ,thus1 for example1 it is possible that life is one long dream1 and that the outer world has only that degree of reality that the objects of dreams have2 but although such a view does not seem inconsistent with known facts1 there is no reason to prefer it to the common-sense view1 according to which other people and things do really exist4 ,thus coherence as the definition of truth fails because there is no proof that there can be only one coherent system4 ,the other objection to this definition of truth is that it assumes the meaning of 'coherence' known1 whereas1 in fact1 'coherence' presupposes the truth of the laws of logic4 ,two propositions are coherent when both may be true1 and are incoherent when one at least must be false4 ,now in order to know whether two propositions can both be true1 we must know such truths as the law of contradiction4 ,for example1 the two propositions1 'this tree is a beech' and 'this tree is not a beech'1 are not coherent1 because of the law of contradiction4 ,but if the law of contradiction itself were subjected to the test of coherence1 we should find that1 if we choose to suppose it false1 nothing will any longer be incoherent with anything else4 ,thus the laws of logic supply the skeleton or framework within which the test of coherence applies1 and they themselves cannot be established by this test4 ,for the above two reasons1 coherence cannot be accepted as giving the meaning of truth1 though it is often a most important test of truth after a certain amount of truth has become known4 ,hence we are driven back to correspondence with fact as constituting the nature of truth4 ,it remains to define precisely what we mean by 'fact'1 and what is the nature of the correspondence which must subsist between belief and fact1 in order that belief may be true4 ,in accordance with our three requisites1 we have to seek a theory of truth which 7#a7 allows truth to have an opposite1 namely falsehood1 7#b7 makes truth a property of beliefs1 but 7#c7 makes it a property wholly dependent upon the relation of the beliefs to outside things4 ,the necessity of allowing for falsehood makes it impossible to regard belief as a relation of the mind to a single object1 which could be said to be what is believed4 ,if belief were so regarded1 we should find that1 like acquaintance1 it would not admit of the opposition of truth and falsehood1 but would have to be always true4 ,this may be made clear by examples4 ,othello believes falsely that ,desdemona loves ,cassio4 ,we cannot say that this belief consists in a relation to a single object1 ',desdemona's love for ,cassio'1 for if there were such an object1 the belief would be true4 ,there is in fact no such object1 and therefore ,othello cannot have any relation to such an object4 ,hence his belief cannot possibly consist in a relation to this object4 ,it might be said that his belief is a relation to a different object1 namely 'that ,desdemona loves ,cassio'2 but it is almost as difficult to suppose that there is such an object as this1 when ,desdemona does not love ,cassio1 as it was to suppose that there is ',desdemona's love for ,cassio'4 ,hence it will be better to seek for a theory of belief which does not make it consist in a relation of the mind to a single object4 ,it is common to think of relations as though they always held between two terms1 but in fact this is not always the case4 ,some relations demand three terms1 some four1 and so on4 ,take1 for instance1 the relation 'between'4 ,so long as only two terms come in1 the relation 'between' is impossible3 three terms are the smallest number that render it possible4 ,york is between ,london and ,edinburgh2 but if ,london and ,edinburgh were the only places in the world1 there could be nothing which was between one place and another4 ,similarly jealousy requires three people3 there can be no such relation that does not involve three at least4 ,such a proposition as ',a wishes ,b to promote ,c's marriage with ,d' involves a relation of four terms2 that is to say1 ,a and ,b and ,c and ,d all come in1 and the relation involved cannot be expressed otherwise than in a form involving all four4 ,instances might be multiplied indefinitely1 but enough has been said to show that there are relations which require more than two terms before they can occur4 ,the relation involved in judging or believing must1 if falsehood is to be duly allowed for1 be taken to be a relation between several terms1 not between two4 ,when ,othello believes that ,desdemona loves ,cassio1 he must not have before his mind a single object1 ',desdemona's love for ,cassio'1 or 'that ,desdemona loves ,cassio '1 for that would require that there should be objective falsehoods1 which subsist independently of any minds2 and this1 though not logically refutable1 is a theory to be avoided if possible4 ,thus it is easier to account for falsehood if we take judgement to be a relation in which the mind and the various objects concerned all occur severally2 that is to say1 ,desdemona and loving and ,cassio must all be terms in the relation which subsists when ,othello believes that ,desdemona loves ,cassio4 ,this relation1 therefore1 is a relation of four terms1 since ,othello also is one of the terms of the relation4 ,when we say that it is a relation of four terms1 we do not mean that ,othello has a certain relation to ,desdemona1 and has the same relation to loving and also to ,cassio4 ,this may be true of some other relation than believing2 but believing1 plainly1 is not a relation which ,othello has to each of the three terms concerned1 but to all of them together3 there is only one example of the relation of believing involved1 but this one example knits together four terms4 ,thus the actual occurrence1 at the moment when ,othello is entertaining his belief1 is that the relation called 'believing' is knitting together into one complex whole the four terms ,othello1 ,desdemona1 loving1 and ,cassio4 ,what is called belief or judgement is nothing but this relation of believing or judging1 which relates a mind to several things other than itself4 ,an act of belief or of judgement is the occurrence between certain terms at some particular time1 of the relation of believing or judging4 ,we are now in a position to understand what it is that distinguishes a true judgement from a false one4 ,for this purpose we will adopt certain definitions4 ,in every act of judgement there is a mind which judges1 and there are terms concerning which it judges4 ,we will call the mind the subject in the judgement1 and the remaining terms the objects4 ,thus1 when ,othello judges that ,desdemona loves ,cassio1 ,othello is the subject1 while the objects are ,desdemona and loving and ,cassio4 ,the subject and the objects together are called the constituents of the judgement4 ,it will be observed that the relation of judging has what is called a 'sense' or 'direction'4 ,we may say1 metaphorically1 that it puts its objects in a certain order1 which we may indicate by means of the order of the words in the sentence4 7,in an inflected language1 the same thing will be indicated by inflections1 e4g4 by the difference between nominative and accusative47 ,othello's judgement that ,cassio loves ,desdemona differs from his judgement that ,desdemona loves ,cassio1 in spite of the fact that it consists of the same constituents1 because the relation of judging places the constituents in a different order in the two cases4 ,similarly1 if ,cassio judges that ,desdemona loves ,othello1 the constituents of the judgement are still the same1 but their order is different4 ,this property of having a 'sense' or 'direction' is one which the relation of judging shares with all other relations4 ,the 'sense' of relations is the ultimate source of order and series and a host of mathematical concepts2 but we need not concern ourselves further with this aspect4 ,we spoke of the relation called 'judging' or 'believing' as knitting together into one complex whole the subject and the objects4 ,in this respect1 judging is exactly like every other relation4 ,whenever a relation holds between two or more terms1 it unites the terms into a complex whole4 ,if ,othello loves ,desdemona1 there is such a complex whole as ',othello's love for ,desdemona'4 ,the terms united by the relation may be themselves complex1 or may be simple1 but the whole which results from their being united must be complex4 ,wherever there is a relation which relates certain terms1 there is a complex object formed of the union of those terms2 and conversely1 wherever there is a complex object1 there is a relation which relates its constituents4 ,when an act of believing occurs1 there is a complex1 in which 'believing' is the uniting relation1 and subject and objects are arranged in a certain order by the 'sense' of the relation of believing4 ,among the objects1 as we saw in considering ',othello believes that ,desdemona loves ,cassio'1 one must be a relation--in this instance1 the relation 'loving'4 ,but this relation1 as it occurs in the act of believing1 is not the relation which creates the unity of the complex whole consisting of the subject and the objects4 ,the relation 'loving'1 as it occurs in the act of believing1 is one of the objects--it is a brick in the structure1 not the cement4 ,the cement is the relation 'believing'4 ,when the belief is true1 there is another complex unity1 in which the relation which was one of the objects of the belief relates the other objects4 ,thus1 e4g41 if ,othello believes truly that ,desdemona loves ,cassio1 then there is a complex unity1 ',desdemona's love for ,cassio'1 which is composed exclusively of the objects of the belief1 in the same order as they had in the belief1 with the relation which was one of the objects occurring now as the cement that binds together the other objects of the belief4 ,on the other hand1 when a belief is false1 there is no such complex unity composed only of the objects of the belief4 ,if ,othello believes falsely that ,desdemona loves ,cassio1 then there is no such complex unity as ',desdemona's love for ,cassio'4 ,thus a belief is true when it corresponds to a certain associated complex1 and false when it does not4 ,assuming1 for the sake of definiteness1 that the objects of the belief are two terms and a relation1 the terms being put in a certain order by the 'sense' of the believing1 then if the two terms in that order are united by the relation into a complex1 the belief is true2 if not1 it is false4 ,this constitutes the definition of truth and falsehood that we were in search of4 ,judging or believing is a certain complex unity of which a mind is a constituent2 if the remaining constituents1 taken in the order which they have in the belief1 form a complex unity1 then the belief is true2 if not1 it is false4 ,thus although truth and falsehood are properties of beliefs1 yet they are in a sense extrinsic properties1 for the condition of the truth of a belief is something not involving beliefs1 or 7in general7 any mind at all1 but only the objects of the belief4 ,a mind1 which believes1 believes truly when there is a corresponding complex not involving the mind1 but only its objects4 ,this correspondence ensures truth1 and its absence entails falsehood4 ,hence we account simultaneously for the two facts that beliefs 7a7 depend on minds for their existence1 7b7 do not depend on minds for their truth4 ,we may restate our theory as follows3 ,if we take such a belief as ',othello believes that ,desdemona loves ,cassio'1 we will call ,desdemona and ,cassio the object-terms1 and loving the object-relation4 ,if there is a complex unity ',desdemona's love for ,cassio'1 consisting of the object-terms related by the object-relation in the same order as they have in the belief1 then this complex unity is called the fact corresponding to the belief4 ,thus a belief is true when there is a corresponding fact1 and is false when there is no corresponding fact4 ,it will be seen that minds do not create truth or falsehood4 ,they create beliefs1 but when once the beliefs are created1 the mind cannot make them true or false1 except in the special case where they concern future things which are within the power of the person believing1 such as catching trains4 ,what makes a belief true is a fact1 and this fact does not 7except in exceptional cases7 in any way involve the mind of the person who has the belief4 ,having now decided what we mean by truth and falsehood1 we have next to consider what ways there are of knowing whether this or that belief is true or false4 ,this consideration will occupy the next chapter4 ,,chapter ,,xiii4 ,,knowledge1 ,,error1 ,,and ,,probable ,,opinion ,the question as to what we mean by truth and falsehood1 which we considered in the preceding chapter1 is of much less interest than the question as to how we can know what is true and what is false4 ,this question will occupy us in the present chapter4 ,there can be no doubt that some of our beliefs are erroneous2 thus we are led to inquire what certainty we can ever have that such and such a belief is not erroneous4 ,in other words1 can we ever know anything at all1 or do we merely sometimes by good luck believe what is true8 ,before we can attack this question1 we must1 however1 first decide what we mean by 'knowing'1 and this question is not so easy as might be supposed4 ,at first sight we might imagine that knowledge could be defined as 'true belief'4 ,when what we believe is true1 it might be supposed that we had achieved a knowledge of what we believe4 ,but this would not accord with the way in which the word is commonly used4 ,to take a very trivial instance3 ,if a man believes that the late ,prime ,minister's last name began with a ,b1 he believes what is true1 since the late ,prime ,minister was ,sir ,henry ,campbell ,bannerman4 ,but if he believes that ,mr4 ,balfour was the late ,prime ,minister1 he will still believe that the late ,prime ,minister's last name began with a ,b1 yet this belief1 though true1 would not be thought to constitute knowledge4 ,if a newspaper1 by an intelligent anticipation1 announces the result of a battle before any telegram giving the result has been received1 it may by good fortune announce what afterwards turns out to be the right result1 and it may produce belief in some of its less experienced readers4 ,but in spite of the truth of their belief1 they cannot be said to have knowledge4 ,thus it is clear that a true belief is not knowledge when it is deduced from a false belief4 ,in like manner1 a true belief cannot be called knowledge when it is deduced by a fallacious process of reasoning1 even if the premisses from which it is deduced are true4 ,if ,i know that all ,greeks are men and that ,socrates was a man1 and ,i infer that ,socrates was a ,greek1 ,i cannot be said to know that ,socrates was a ,greek1 because1 although my premisses and my conclusion are true1 the conclusion does not follow from the premisses4 ,but are we to say that nothing is knowledge except what is validly deduced from true premisses8 ,obviously we cannot say this4 ,such a definition is at once too wide and too narrow4 ,in the first place1 it is too wide1 because it is not enough that our premisses should be true1 they must also be known4 ,the man who believes that ,mr4 ,balfour was the late ,prime ,minister may proceed to draw valid deductions from the true premiss that the late ,prime ,minister's name began with a ,b1 but he cannot be said to know the conclusions reached by these deductions4 ,thus we shall have to amend our definition by saying that knowledge is what is validly deduced from known premisses4 ,this1 however1 is a circular definition3 it assumes that we already know what is meant by 'known premisses'4 ,it can1 therefore1 at best define one sort of knowledge1 the sort we call derivative1 as opposed to intuitive knowledge4 ,we may say3 ',derivative knowledge is what is validly deduced from premisses known intuitively'4 ,in this statement there is no formal defect1 but it leaves the definition of intuitive knowledge still to seek4 ,leaving on one side1 for the moment1 the question of intuitive knowledge1 let us consider the above suggested definition of derivative knowledge4 ,the chief objection to it is that it unduly limits knowledge4 ,it constantly happens that people entertain a true belief1 which has grown up in them because of some piece of intuitive knowledge from which it is capable of being validly inferred1 but from which it has not1 as a matter of fact1 been inferred by any logical process4 ,take1 for example1 the beliefs produced by reading4 ,if the newspapers announce the death of the ,king1 we are fairly well justified in believing that the ,king is dead1 since this is the sort of announcement which would not be made if it were false4 ,and we are quite amply justified in believing that the newspaper asserts that the ,king is dead4 ,but here the intuitive knowledge upon which our belief is based is knowledge of the existence of sense-data derived from looking at the print which gives the news4 ,this knowledge scarcely rises into consciousness1 except in a person who cannot read easily4 ,a child may be aware of the shapes of the letters1 and pass gradually and painfully to a realization of their meaning4 ,but anybody accustomed to reading passes at once to what the letters mean1 and is not aware1 except on reflection1 that he has derived this knowledge from the sense-data called seeing the printed letters4 ,thus although a valid inference from the-letters to their meaning is possible1 and could be performed by the reader1 it is not in fact performed1 since he does not in fact perform any operation which can be called logical inference4 ,yet it would be absurd to say that the reader does not know that the newspaper announces the ,king's death4 ,we must1 therefore1 admit as derivative knowledge whatever is the result of intuitive knowledge even if by mere association1 provided there is a valid logical connexion1 and the person in question could become aware of this connexion by reflection4 ,there are in fact many ways1 besides logical inference1 by which we pass from one belief to another3 the passage from the print to its meaning illustrates these ways4 ,these ways may be called 'psychological inference'4 ,we shall1 then1 admit such psychological inference as a means of obtaining derivative knowledge1 provided there is a discoverable logical inference which runs parallel to the psychological inference4 ,this renders our definition of derivative knowledge less precise than we could wish1 since the word 'discoverable' is vague3 it does not tell us how much reflection may be needed in order to make the discovery4 ,but in fact 'knowledge' is not a precise conception3 it merges into 'probable opinion'1 as we shall see more fully in the course of the present chapter4 ,a very precise definition1 therefore1 should not be sought1 since any such definition must be more or less misleading4 ,the chief difficulty in regard to knowledge1 however1 does not arise over derivative knowledge1 but over intuitive knowledge4 ,so long as we are dealing with derivative knowledge1 we have the test of intuitive knowledge to fall back upon4 ,but in regard to intuitive beliefs1 it is by no means easy to discover any criterion by which to distinguish some as true and others as erroneous4 ,in this question it is scarcely possible to reach any very precise result3 all our knowledge of truths is infected with some degree of doubt1 and a theory which ignored this fact would be plainly wrong4 ,something may be done1 however1 to mitigate the difficulties of the question4 ,our theory of truth1 to begin with1 supplies the possibility of distinguishing certain truths as self-evident in a sense which ensures infallibility4 ,when a belief is true1 we said1 there is a corresponding fact1 in which the several objects of the belief form a single complex4 ,the belief is said to constitute knowledge of this fact1 provided it fulfils those further somewhat vague conditions which we have been considering in the present chapter4 ,but in regard to any fact1 besides the knowledge constituted by belief1 we may also have the kind of knowledge constituted by perception 7taking this word in its widest possible sense74 ,for example1 if you know the hour of the sunset1 you can at that hour know the fact that the sun is setting3 this is knowledge of the fact by way of knowledge of truths2 but you can also1 if the weather is fine1 look to the west and actually see the setting sun3 you then know the same fact by the way of knowledge of things4 ,thus in regard to any complex fact1 there are1 theoretically1 two ways in which it may be known3 7#a7 by means of a judgement1 in which its several parts are judged to be related as they are in fact related2 7#b7 by means of acquaintance with the complex fact itself1 which may 7in a large sense7 be called perception1 though it is by no means confined to objects of the senses4 ,now it will be observed that the second way of knowing a complex fact1 the way of acquaintance1 is only possible when there really is such a fact1 while the first way1 like all judgement1 is liable to error4 ,the second way gives us the complex whole1 and is therefore only possible when its parts do actually have that relation which makes them combine to form such a complex4 ,the first way1 on the contrary1 gives us the parts and the relation severally1 and demands only the reality of the parts and the relation3 the relation may not relate those parts in that way1 and yet the judgement may occur4 ,it will be remembered that at the end of ,chapter ,,xi we suggested that there might be two kinds of self-evidence1 one giving an absolute guarantee of truth1 the other only a partial guarantee4 ,these two kinds can now be distinguished4 ,we may say that a truth is self-evident1 in the first and most absolute sense1 when we have acquaintance with the fact which corresponds to the truth4 ,when ,othello believes that ,desdemona loves ,cassio1 the corresponding fact1 if his belief were true1 would be ',desdemona's love for ,cassio'4 ,this would be a fact with which no one could have acquaintance except ,desdemona2 hence in the sense of self-evidence that we are considering1 the truth that ,desdemona loves ,cassio 7if it were a truth7 could only be self-evident to ,desdemona4 ,all mental facts1 and all facts concerning sense-data1 have this same privacy3 there is only one person to whom they can be self-evident in our present sense1 since there is only one person who can be acquainted with the mental things or the sense-data concerned4 ,thus no fact about any particular existing thing can be self-evident to more than one person4 ,on the other hand1 facts about universals do not have this privacy4 ,many minds may be acquainted with the same universals2 hence a relation between universals may be known by acquaintance to many different people4 ,in all cases where we know by acquaintance a complex fact consisting of certain terms in a certain relation1 we say that the truth that these terms are so related has the first or absolute kind of self-evidence1 and in these cases the judgement that the terms are so related must be true4 ,thus this sort of self-evidence is an absolute guarantee of truth4 ,but although this sort of self-evidence is an absolute guarantee of truth1 it does not enable us to be absolutely certain1 in the case of any given judgement1 that the judgement in question is true4 ,suppose we first perceive the sun shining1 which is a complex fact1 and thence proceed to make the judgement 'the sun is shining'4 ,in passing from the perception to the judgement1 it is necessary to analyse the given complex fact3 we have to separate out 'the sun' and 'shining' as constituents of the fact4 ,in this process it is possible to commit an error2 hence even where a fact has the first or absolute kind of self-evidence1 a judgement believed to correspond to the fact is not absolutely infallible1 because it may not really correspond to the fact4 ,but if it does correspond 7in the sense explained in the preceding chapter71 then it must be true4 ,the second sort of self-evidence will be that which belongs to judgements in the first instance1 and is not derived from direct perception of a fact as a single complex whole4 ,this second kind of self-evidence will have degrees1 from the very highest degree down to a bare inclination in favour of the belief4 ,take1 for example1 the case of a horse trotting away from us along a hard road4 ,at first our certainty that we hear the hoofs is complete2 gradually1 if we listen intently1 there comes a moment when we think perhaps it was imagination or the blind upstairs or our own heartbeats2 at last we become doubtful whether there was any noise at all2 then we think we no longer hear anything1 and at last we know we no longer hear anything4 ,in this process1 there is a continual gradation of self-evidence1 from the highest degree to the least1 not in the sense-data themselves1 but in the judgements based on them4 ,or again3 ,suppose we are comparing two shades of colour1 one blue and one green4 ,we can be quite sure they are different shades of colour2 but if the green colour is gradually altered to be more and more like the blue1 becoming first a blue-green1 then a greeny-blue1 then blue1 there will come a moment when we are doubtful whether we can see any difference1 and then a moment when we know that we cannot see any difference4 ,the same thing happens in tuning a musical instrument1 or in any other case where there is a continuous gradation4 ,thus self-evidence of this sort is a matter of degree2 and it seems plain that the higher degrees are more to be trusted than the lower degrees4 ,in derivative knowledge our ultimate premisses must have some degree of self-evidence1 and so must their connexion with the conclusions deduced from them4 ,take for example a piece of reasoning in geometry4 ,it is not enough that the axioms from which we start should be self-evident3 it is necessary also that1 at each step in the reasoning1 the connexion of premiss and conclusion should be self-evident4 ,in difficult reasoning1 this connexion has often only a very small degree of self-evidence2 hence errors of reasoning are not improbable where the difficulty is great4 ,from what has been said it is evident that1 both as regards intuitive knowledge and as regards derivative knowledge1 if we assume that intuitive knowledge is trustworthy in proportion to the degree of its self-evidence1 there will be a gradation in trustworthiness1 from the existence of noteworthy sense-data and the simpler truths of logic and arithmetic1 which may be taken as quite certain1 down to judgements which seem only just more probable than their opposites4 ,what we firmly believe1 if it is true1 is called knowledge1 provided it is either intuitive or inferred 7logically or psychologically7 from intuitive knowledge from which it follows logically4 ,what we firmly believe1 if it is not true1 is called error4 ,what we firmly believe1 if it is neither knowledge nor error1 and also what we believe hesitatingly1 because it is1 or is derived from1 something which has not the highest degree of self-evidence1 may be called probable opinion4 ,thus the greater part of what would commonly pass as knowledge is more or less probable opinion4 ,in regard to probable opinion1 we can derive great assistance from coherence1 which we rejected as the definition of truth1 but may often use as a criterion4 ,a body of individually probable opinions1 if they are mutually coherent1 become more probable than any one of them would be individually4 ,it is in this way that many scientific hypotheses acquire their probability4 ,they fit into a coherent system of probable opinions1 and thus become more probable than they would be in isolation4 ,the same thing applies to general philosophical hypotheses4 ,often in a single case such hypotheses may seem highly doubtful1 while yet1 when we consider the order and coherence which they introduce into a mass of probable opinion1 they become pretty nearly certain4 ,this applies1 in particular1 to such matters as the distinction between dreams and waking life4 ,if our dreams1 night after night1 were as coherent one with another as our days1 we should hardly know whether to believe the dreams or the waking life4 ,as it is1 the test of coherence condemns the dreams and confirms the waking life4 ,but this test1 though it increases probability where it is successful1 never gives absolute certainty1 unless there is certainty already at some point in the coherent system4 ,thus the mere organization of probable opinion will never1 by itself1 transform it into indubitable knowledge4 ,,chapter ,,xiv4 ,,the ,,limits ,,of ,,philosophical ,,knowledge ,in all that we have said hitherto concerning philosophy1 we have scarcely touched on many matters that occupy a great space in the writings of most philosophers4 ,most philosophers--or1 at any rate1 very many--profess to be able to prove1 by a priori metaphysical reasoning1 such things as the fundamental dogmas of religion1 the essential rationality of the universe1 the illusoriness of matter1 the unreality of all evil1 and so on4 ,there can be no doubt that the hope of finding reason to believe such theses as these has been the chief inspiration of many life-long students of philosophy4 ,this hope1 ,i believe1 is vain4 ,it would seem that knowledge concerning the universe as a whole is not to be obtained by metaphysics1 and that the proposed proofs that1 in virtue of the laws of logic such and such things must exist and such and such others cannot1 are not capable of surviving a critical scrutiny4 ,in this chapter we shall briefly consider the kind of way in which such reasoning is attempted1 with a view to discovering whether we can hope that it may be valid4 ,the great representative1 in modern times1 of the kind of view which we wish to examine1 was ,hegel 7#aggj-ahca74 ,hegel's philosophy is very difficult1 and commentators differ as to the true interpretation of it4 ,according to the interpretation ,i shall adopt1 which is that of many1 if not most1 of the commentators and has the merit of giving an interesting and important type of philosophy1 his main thesis is that everything short of the ,whole is obviously fragmentary1 and obviously incapable of existing without the complement supplied by the rest of the world4 ,just as a comparative anatomist1 from a single bone1 sees what kind of animal the whole must have been1 so the metaphysician1 according to ,hegel1 sees1 from any one piece of reality1 what the whole of reality must be--at least in its large outlines4 ,every apparently separate piece of reality has1 as it were1 hooks which grapple it to the next piece2 the next piece1 in turn1 has fresh hooks1 and so on1 until the whole universe is reconstructed4 ,this essential incompleteness appears1 according to ,hegel1 equally in the world of thought and in the world of things4 ,in the world of thought1 if we take any idea which is abstract or incomplete1 we find1 on examination1 that if we forget its incompleteness1 we become involved in contradictions2 these contradictions turn the idea in question into its opposite1 or antithesis2 and in order to escape1 we have to find a new1 less incomplete idea1 which is the synthesis of our original idea and its antithesis4 ,this new idea1 though less incomplete than the idea we started with1 will be found1 nevertheless1 to be still not wholly complete1 but to pass into its antithesis1 with which it must be combined in a new synthesis4 ,in this way ,hegel advances until he reaches the ',absolute ,idea'1 which1 according to him1 has no incompleteness1 no opposite1 and no need of further development4 ,the ,absolute ,idea1 therefore1 is adequate to describe ,absolute ,reality2 but all lower ideas only describe reality as it appears to a partial view1 not as it is to one who simultaneously surveys the ,whole4 ,thus ,hegel reaches the conclusion that ,absolute ,reality forms one single harmonious system1 not in space or time1 not in any degree evil1 wholly rational1 and wholly spiritual4 ,any appearance to the contrary1 in the world we know1 can be proved logically--so he believes--to be entirely due to our fragmentary piecemeal view of the universe4 ,if we saw the universe whole1 as we may suppose ,god sees it1 space and time and matter and evil and all striving and struggling would disappear1 and we should see instead an eternal perfect unchanging spiritual unity4 ,in this conception1 there is undeniably something sublime1 something to which we could wish to yield assent4 ,nevertheless1 when the arguments in support of it are carefully examined1 they appear to involve much confusion and many unwarrantable assumptions4 ,the fundamental tenet upon which the system is built up is that what is incomplete must be not self-subsistent1 but must need the support of other things before it can exist4 ,it is held that whatever has relations to things outside itself must contain some reference to those outside things in its own nature1 and could not1 therefore1 be what it is if those outside things did not exist4 ,a man's nature1 for example1 is constituted by his memories and the rest of his knowledge1 by his loves and hatreds1 and so on2 thus1 but for the objects which he knows or loves or hates1 he could not be what he is4 ,he is essentially and obviously a fragment3 taken as the sum-total of reality he would be self-contradictory4 ,this whole point of view1 however1 turns upon the notion of the 'nature' of a thing1 which seems to mean 'all the truths about the thing'4 ,it is of course the case that a truth which connects one thing with another thing could not subsist if the other thing did not subsist4 ,but a truth about a thing is not part of the thing itself1 although it must1 according to the above usage1 be part of the 'nature' of the thing4 ,if we mean by a thing's 'nature' all the truths about the thing1 then plainly we cannot know a thing's 'nature' unless we know all the thing's relations to all the other things in the universe4 ,but if the word 'nature' is used in this sense1 we shall have to hold that the thing may be known when its 'nature' is not known1 or at any rate is not known completely4 ,there is a confusion1 when this use of the word 'nature' is employed1 between knowledge of things and knowledge of truths4 ,we may have knowledge of a thing by acquaintance even if we know very few propositions about it--theoretically we need not know any propositions about it4 ,thus1 acquaintance with a thing does not involve knowledge of its 'nature' in the above sense4 ,and although acquaintance with a thing is involved in our knowing any one proposition about a thing1 knowledge of its 'nature'1 in the above sense1 is not involved4 ,hence1 7#a7 acquaintance with a thing does not logically involve a knowledge of its relations1 and 7#b7 a knowledge of some of its relations does not involve a knowledge of all of its relations nor a knowledge of its 'nature' in the above sense4 ,i may be acquainted1 for example1 with my toothache1 and this knowledge may be as complete as knowledge by acquaintance ever can be1 without knowing all that the dentist 7who is not acquainted with it7 can tell me about its cause1 and without therefore knowing its 'nature' in the above sense4 ,thus the fact that a thing has relations does not prove that its relations are logically necessary4 ,that is to say1 from the mere fact that it is the thing it is we cannot deduce that it must have the various relations which in fact it has4 ,this only seems to follow because we know it already4 ,it follows that we cannot prove that the universe as a whole forms a single harmonious system such as ,hegel believes that it forms4 ,and if we cannot prove this1 we also cannot prove the unreality of space and time and matter and evil1 for this is deduced by ,hegel from the fragmentary and relational character of these things4 ,thus we are left to the piecemeal investigation of the world1 and are unable to know the characters of those parts of the universe that are remote from our experience4 ,this result1 disappointing as it is to those whose hopes have been raised by the systems of philosophers1 is in harmony with the inductive and scientific temper of our age1 and is borne out by the whole examination of human knowledge which has occupied our previous chapters4 ,most of the great ambitious attempts of metaphysicians have proceeded by the attempt to prove that such and such apparent features of the actual world were self-contradictory1 and therefore could not be real4 ,the whole tendency of modern thought1 however1 is more and more in the direction of showing that the supposed contradictions were illusory1 and that very little can be proved a priori from considerations of what must be4 ,a good illustration of this is afforded by space and time4 ,space and time appear to be infinite in extent1 and infinitely divisible4 ,if we travel along a straight line in either direction1 it is difficult to believe that we shall finally reach a last point1 beyond which there is nothing1 not even empty space4 ,similarly1 if in imagination we travel backwards or forwards in time1 it is difficult to believe that we shall reach a first or last time1 with not even empty time beyond it4 ,thus space and time appear to be infinite in extent4 ,again1 if we take any two points on a line1 it seems evident that there must be other points between them however small the distance between them may be3 every distance can be halved1 and the halves can be halved again1 and so on ad infinitum4 ,in time1 similarly1 however little time may elapse between two moments1 it seems evident that there will be other moments between them4 ,thus space and time appear to be infinitely divisible4 ,but as against these apparent facts--infinite extent and infinite divisibility--philosophers have advanced arguments tending to show that there could be no infinite collections of things1 and that therefore the number of points in space1 or of instants in time1 must be finite4 ,thus a contradiction emerged between the apparent nature of space and time and the supposed impossibility of infinite collections4 ,kant1 who first emphasized this contradiction1 deduced the impossibility of space and time1 which he declared to be merely subjective2 and since his time very many philosophers have believed that space and time are mere appearance1 not characteristic of the world as it really is4 ,now1 however1 owing to the labours of the mathematicians1 notably ,georg ,cantor1 it has appeared that the impossibility of infinite collections was a mistake4 ,they are not in fact self-contradictory1 but only contradictory of certain rather obstinate mental prejudices4 ,hence the reasons for regarding space and time as unreal have become inoperative1 and one of the great sources of metaphysical constructions is dried up4 ,the mathematicians1 however1 have not been content with showing that space as it is commonly supposed to be is possible2 they have shown also that many other forms of space are equally possible1 so far as logic can show4 ,some of ,euclid's axioms1 which appear to common sense to be necessary1 and were formerly supposed to be necessary by philosophers1 are now known to derive their appearance of necessity from our mere familiarity with actual space1 and not from any a priori logical foundation4 ,by imagining worlds in which these axioms are false1 the mathematicians have used logic to loosen the prejudices of common sense1 and to show the possibility of spaces differing--some more1 some less--from that in which we live4 ,and some of these spaces differ so little from ,euclidean space1 where distances such as we can measure are concerned1 that it is impossible to discover by observation whether our actual space is strictly ,euclidean or of one of these other kinds4 ,thus the position is completely reversed4 ,formerly it appeared that experience left only one kind of space to logic1 and logic showed this one kind to be impossible4 ,now1 logic presents many kinds of space as possible apart from experience1 and experience only partially decides between them4 ,thus1 while our knowledge of what is has become less than it was formerly supposed to be1 our knowledge of what may be is enormously increased4 ,instead of being shut in within narrow walls1 of which every nook and cranny could be explored1 we find ourselves in an open world of free possibilities1 where much remains unknown because there is so much to know4 ,what has happened in the case of space and time has happened1 to some extent1 in other directions as well4 ,the attempt to prescribe to the universe by means of a priori principles has broken down2 logic1 instead of being1 as formerly1 the bar to possibilities1 has become the great liberator of the imagination1 presenting innumerable alternatives which are closed to unreflective common sense1 and leaving to experience the task of deciding1 where decision is possible1 between the many worlds which logic offers for our choice4 ,thus knowledge as to what exists becomes limited to what we can learn from experience--not to what we can actually experience1 for1 as we have seen1 there is much knowledge by description concerning things of which we have no direct experience4 ,but in all cases of knowledge by description1 we need some connexion of universals1 enabling us1 from such and such a datum1 to infer an object of a certain sort as implied by our datum4 ,thus in regard to physical objects1 for example1 the principle that sense-data are signs of physical objects is itself a connexion of universals2 and it is only in virtue of this principle that experience enables us to acquire knowledge concerning physical objects4 ,the same applies to the law of causality1 or1 to descend to what is less general1 to such principles as the law of gravitation4 ,principles such as the law of gravitation are proved1 or rather are rendered highly probable1 by a combination of experience with some wholly a priori principle1 such as the principle of induction4 ,thus our intuitive knowledge1 which is the source of all our other knowledge of truths1 is of two sorts3 pure empirical knowledge1 which tells us of the existence and some of the properties of particular things with which we are acquainted1 and pure a priori knowledge1 which gives us connexions between universals1 and enables us to draw inferences from the particular facts given in empirical knowledge4 ,our derivative knowledge always depends upon some pure a priori knowledge and usually also depends upon some pure empirical knowledge4 ,philosophical knowledge1 if what has been said above is true1 does not differ essentially from scientific knowledge2 there is no special source of wisdom which is open to philosophy but not to science1 and the results obtained by philosophy are not radically different from those obtained from science4 ,the essential characteristic of philosophy1 which makes it a study distinct from science1 is criticism4 ,it examines critically the principles employed in science and in daily life2 it searches out any inconsistencies there may be in these principles1 and it only accepts them when1 as the result of a critical inquiry1 no reason for rejecting them has appeared4 ,if1 as many philosophers have believed1 the principles underlying the sciences were capable1 when disengaged from irrelevant detail1 of giving us knowledge concerning the universe as a whole1 such knowledge would have the same claim on our belief as scientific knowledge has2 but our inquiry has not revealed any such knowledge1 and therefore1 as regards the special doctrines of the bolder metaphysicians1 has had a mainly negative result4 ,but as regards what would be commonly accepted as knowledge1 our result is in the main positive3 we have seldom found reason to reject such knowledge as the result of our criticism1 and we have seen no reason to suppose man incapable of the kind of knowledge which he is generally believed to possess4 ,when1 however1 we speak of philosophy as a criticism of knowledge1 it is necessary to impose a certain limitation4 ,if we adopt the attitude of the complete sceptic1 placing ourselves wholly outside all knowledge1 and asking1 from this outside position1 to be compelled to return within the circle of knowledge1 we are demanding what is impossible1 and our scepticism can never be refuted4 ,for all refutation must begin with some piece of knowledge which the disputants share2 from blank doubt1 no argument can begin4 ,hence the criticism of knowledge which philosophy employs must not be of this destructive kind1 if any result is to be achieved4 ,against this absolute scepticism1 no logical argument can be advanced4 ,but it is not difficult to see that scepticism of this kind is unreasonable4 ,descartes' 'methodical doubt'1 with which modern philosophy began1 is not of this kind1 but is rather the kind of criticism which we are asserting to be the essence of philosophy4 ,his 'methodical doubt' consisted in doubting whatever seemed doubtful2 in pausing1 with each apparent piece of knowledge1 to ask himself whether1 on reflection1 he could feel certain that he really knew it4 ,this is the kind of criticism which constitutes philosophy4 ,some knowledge1 such as knowledge of the existence of our sense-data1 appears quite indubitable1 however calmly and thoroughly we reflect upon it4 ,in regard to such knowledge1 philosophical criticism does not require that we should abstain from belief4 ,but there are beliefs--such1 for example1 as the belief that physical objects exactly resemble our sense-data--which are entertained until we begin to reflect1 but are found to melt away when subjected to a close inquiry4 ,such beliefs philosophy will bid us reject1 unless some new line of argument is found to support them4 ,but to reject the beliefs which do not appear open to any objections1 however closely we examine them1 is not reasonable1 and is not what philosophy advocates4 ,the criticism aimed at1 in a word1 is not that which1 without reason1 determines to reject1 but that which considers each piece of apparent knowledge on its merits1 and retains whatever still appears to be knowledge when this consideration is completed4 ,that some risk of error remains must be admitted1 since human beings are fallible4 ,philosophy may claim justly that it diminishes the risk of error1 and that in some cases it renders the risk so small as to be practically negligible4 ,to do more than this is not possible in a world where mistakes must occur2 and more than this no prudent advocate of philosophy would claim to have performed4 ,,chapter ,,xv4 ,,the ,,value ,,of ,,philosophy ,having now come to the end of our brief and very incomplete review of the problems of philosophy1 it will be well to consider1 in conclusion1 what is the value of philosophy and why it ought to be studied4 ,it is the more necessary to consider this question1 in view of the fact that many men1 under the influence of science or of practical affairs1 are inclined to doubt whether philosophy is anything better than innocent but useless trifling1 hair-splitting distinctions1 and controversies on matters concerning which knowledge is impossible4 ,this view of philosophy appears to result1 partly from a wrong conception of the ends of life1 partly from a wrong conception of the kind of goods which philosophy strives to achieve4 ,physical science1 through the medium of inventions1 is useful to innumerable people who are wholly ignorant of it2 thus the study of physical science is to be recommended1 not only1 or primarily1 because of the effect on the student1 but rather because of the effect on mankind in general4 ,thus utility does not belong to philosophy4 ,if the study of philosophy has any value at all for others than students of philosophy1 it must be only indirectly1 through its effects upon the lives of those who study it4 ,it is in these effects1 therefore1 if anywhere1 that the value of philosophy must be primarily sought4 ,but further1 if we are not to fail in our endeavour to determine the value of philosophy1 we must first free our minds from the prejudices of what are wrongly called 'practical' men4 ,the 'practical' man1 as this word is often used1 is one who recognizes only material needs1 who realizes that men must have food for the body1 but is oblivious of the necessity of providing food for the mind4 ,if all men were well off1 if poverty and disease had been reduced to their lowest possible point1 there would still remain much to be done to produce a valuable society2 and even in the existing world the goods of the mind are at least as important as the goods of the body4 ,it is exclusively among the goods of the mind that the value of philosophy is to be found2 and only those who are not indifferent to these goods can be persuaded that the study of philosophy is not a waste of time4 ,philosophy1 like all other studies1 aims primarily at knowledge4 ,the knowledge it aims at is the kind of knowledge which gives unity and system to the body of the sciences1 and the kind which results from a critical examination of the grounds of our convictions1 prejudices1 and beliefs4 ,but it cannot be maintained that philosophy has had any very great measure of success in its attempts to provide definite answers to its questions4 ,if you ask a mathematician1 a mineralogist1 a historian1 or any other man of learning1 what definite body of truths has been ascertained by his science1 his answer will last as long as you are willing to listen4 ,but if you put the same question to a philosopher1 he will1 if he is candid1 have to confess that his study has not achieved positive results such as have been achieved by other sciences4 ,it is true that this is partly accounted for by the fact that1 as soon as definite knowledge concerning any subject becomes possible1 this subject ceases to be called philosophy1 and becomes a separate science4 ,the whole study of the heavens1 which now belongs to astronomy1 was once included in philosophy2 ,newton's great work was called 'the mathematical principles of natural philosophy'4 ,similarly1 the study of the human mind1 which was a part of philosophy1 has now been separated from philosophy and has become the science of psychology4 ,thus1 to a great extent1 the uncertainty of philosophy is more apparent than real3 those questions which are already capable of definite answers are placed in the sciences1 while those only to which1 at present1 no definite answer can be given1 remain to form the residue which is called philosophy4 ,this is1 however1 only a part of the truth concerning the uncertainty of philosophy4 ,there are many questions--and among them those that are of the profoundest interest to our spiritual life--which1 so far as we can see1 must remain insoluble to the human intellect unless its powers become of quite a different order from what they are now4 ,has the universe any unity of plan or purpose1 or is it a fortuitous concourse of atoms8 ,is consciousness a permanent part of the universe1 giving hope of indefinite growth in wisdom1 or is it a transitory accident on a small planet on which life must ultimately become impossible8 ,are good and evil of importance to the universe or only to man8 ,such questions are asked by philosophy1 and variously answered by various philosophers4 ,but it would seem that1 whether answers be otherwise discoverable or not1 the answers suggested by philosophy are none of them demonstrably true4 ,yet1 however slight may be the hope of discovering an answer1 it is part of the business of philosophy to continue the consideration of such questions1 to make us aware of their importance1 to examine all the approaches to them1 and to keep alive that speculative interest in the universe which is apt to be killed by confining ourselves to definitely ascertainable knowledge4 ,many philosophers1 it is true1 have held that philosophy could establish the truth of certain answers to such fundamental questions4 ,they have supposed that what is of most importance in religious beliefs could be proved by strict demonstration to be true4 ,in order to judge of such attempts1 it is necessary to take a survey of human knowledge1 and to form an opinion as to its methods and its limitations4 ,on such a subject it would be unwise to pronounce dogmatically2 but if the investigations of our previous chapters have not led us astray1 we shall be compelled to renounce the hope of finding philosophical proofs of religious beliefs4 ,we cannot1 therefore1 include as part of the value of philosophy any definite set of answers to such questions4 ,hence1 once more1 the value of philosophy must not depend upon any supposed body of definitely ascertainable knowledge to be acquired by those who study it4 ,the value of philosophy is1 in fact1 to be sought largely in its very uncertainty4 ,the man who has no tincture of philosophy goes through life imprisoned in the prejudices derived from common sense1 from the habitual beliefs of his age or his nation1 and from convictions which have grown up in his mind without the co-operation or consent of his deliberate reason4 ,to such a man the world tends to become definite1 finite1 obvious2 common objects rouse no questions1 and unfamiliar possibilities are contemptuously rejected4 ,as soon as we begin to philosophize1 on the contrary1 we find1 as we saw in our opening chapters1 that even the most everyday things lead to problems to which only very incomplete answers can be given4 ,philosophy1 though unable to tell us with certainty what is the true answer to the doubts which it raises1 is able to suggest many possibilities which enlarge our thoughts and free them from the tyranny of custom4 ,thus1 while diminishing our feeling of certainty as to what things are1 it greatly increases our knowledge as to what they may be2 it removes the somewhat arrogant dogmatism of those who have never travelled into the region of liberating doubt1 and it keeps alive our sense of wonder by showing familiar things in an unfamiliar aspect4 ,apart from its utility in showing unsuspected possibilities1 philosophy has a value--perhaps its chief value--through the greatness of the objects which it contemplates1 and the freedom from narrow and personal aims resulting from this contemplation4 ,the life of the instinctive man is shut up within the circle of his private interests3 family and friends may be included1 but the outer world is not regarded except as it may help or hinder what comes within the circle of instinctive wishes4 ,in such a life there is something feverish and confined1 in comparison with which the philosophic life is calm and free4 ,the private world of instinctive interests is a small one1 set in the midst of a great and powerful world which must1 sooner or later1 lay our private world in ruins4 ,unless we can so enlarge our interests as to include the whole outer world1 we remain like a garrison in a beleagured fortress1 knowing that the enemy prevents escape and that ultimate surrender is inevitable4 ,in such a life there is no peace1 but a constant strife between the insistence of desire and the powerlessness of will4 ,in one way or another1 if our life is to be great and free1 we must escape this prison and this strife4 ,one way of escape is by philosophic contemplation4 ,philosophic contemplation does not1 in its widest survey1 divide the universe into two hostile camps--friends and foes1 helpful and hostile1 good and bad--it views the whole impartially4 ,philosophic contemplation1 when it is unalloyed1 does not aim at proving that the rest of the universe is akin to man4 ,all acquisition of knowledge is an enlargement of the ,self1 but this enlargement is best attained when it is not directly sought4 ,it is obtained when the desire for knowledge is alone operative1 by a study which does not wish in advance that its objects should have this or that character1 but adapts the ,self to the characters which it finds in its objects4 ,this enlargement of ,self is not obtained when1 taking the ,self as it is1 we try to show that the world is so similar to this ,self that knowledge of it is possible without any admission of what seems alien4 ,the desire to prove this is a form of self-assertion and1 like all self-assertion1 it is an obstacle to the growth of ,self which it desires1 and of which the ,self knows that it is capable4 ,self-assertion1 in philosophic speculation as elsewhere1 views the world as a means to its own ends2 thus it makes the world of less account than ,self1 and the ,self sets bounds to the greatness of its goods4 ,in contemplation1 on the contrary1 we start from the not-,self1 and through its greatness the boundaries of ,self are enlarged2 through the infinity of the universe the mind which contemplates it achieves some share in infinity4 ,for this reason greatness of soul is not fostered by those philosophies which assimilate the universe to ,man4 ,knowledge is a form of union of ,self and not-,self2 like all union1 it is impaired by dominion1 and therefore by any attempt to force the universe into conformity with what we find in ourselves4 ,there is a widespread philosophical tendency towards the view which tells us that ,man is the measure of all things1 that truth is man-made1 that space and time and the world of universals are properties of the mind1 and that1 if there be anything not created by the mind1 it is unknowable and of no account for us4 ,this view1 if our previous discussions were correct1 is untrue2 but in addition to being untrue1 it has the effect of robbing philosophic contemplation of all that gives it value1 since it fetters contemplation to ,self4 ,what it calls knowledge is not a union with the not-,self1 but a set of prejudices1 habits1 and desires1 making an impenetrable veil between us and the world beyond4 ,the man who finds pleasure in such a theory of knowledge is like the man who never leaves the domestic circle for fear his word might not be law4 ,the true philosophic contemplation1 on the contrary1 finds its satisfaction in every enlargement of the not-,self1 in everything that magnifies the objects contemplated1 and thereby the subject contemplating4 ,everything1 in contemplation1 that is personal or private1 everything that depends upon habit1 self-interest1 or desire1 distorts the object1 and hence impairs the union which the intellect seeks4 ,by thus making a barrier between subject and object1 such personal and private things become a prison to the intellect4 ,the free intellect will see as ,god might see1 without a here and now1 without hopes and fears1 without the trammels of customary beliefs and traditional prejudices1 calmly1 dispassionately1 in the sole and exclusive desire of knowledge--knowledge as impersonal1 as purely contemplative1 as it is possible for man to attain4 ,hence also the free intellect will value more the abstract and universal knowledge into which the accidents of private history do not enter1 than the knowledge brought by the senses1 and dependent1 as such knowledge must be1 upon an exclusive and personal point of view and a body whose sense-organs distort as much as they reveal4 ,the mind which has become accustomed to the freedom and impartiality of philosophic contemplation will preserve something of the same freedom and impartiality in the world of action and emotion4 ,it will view its purposes and desires as parts of the whole1 with the absence of insistence that results from seeing them as infinitesimal fragments in a world of which all the rest is unaffected by any one man's deeds4 ,the impartiality which1 in contemplation1 is the unalloyed desire for truth1 is the very same quality of mind which1 in action1 is justice1 and in emotion is that universal love which can be given to all1 and not only to those who are judged useful or admirable4 ,thus contemplation enlarges not only the objects of our thoughts1 but also the objects of our actions and our affections3 it makes us citizens of the universe1 not only of one walled city at war with all the rest4 ,in this citizenship of the universe consists man's true freedom1 and his liberation from the thraldom of narrow hopes and fears4 ,thus1 to sum up our discussion of the value of philosophy2 ,philosophy is to be studied1 not for the sake of any definite answers to its questions1 since no definite answers can1 as a rule1 be known to be true1 but rather for the sake of the questions themselves2 because these questions enlarge our conception of what is possible1 enrich our intellectual imagination and diminish the dogmatic assurance which closes the mind against speculation2 but above all because1 through the greatness of the universe which philosophy contemplates1 the mind also is rendered great1 and becomes capable of that union with the universe which constitutes its highest good4 ,,bibliographical ,,note ,the student who wishes to acquire an elementary knowledge of philosophy will find it both easier and more profitable to read some of the works of the great philosophers than to attempt to derive an all-round view from handbooks4 ,the following are specially recommended3 ,plato3 ,republic1 especially ,books ,,vi and ,,vii4 ,descartes3 ,meditations4 ,spinoza3 ,ethics4 ,leibniz3 ,the ,monadology4 ,berkeley3 ,three ,dialogues between ,hylas and ,philonous4 ,hume3 ,enquiry concerning ,human ,understanding4 ,kant3 ,prolegomena to any ,future ,metaphysic4